The interactive test above draws from this bank in random order. Every question also has its own page with the full explanation.
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Solve for x: 3x + 7 = 22
- x = 5 ✓
- x = 7
- x = 15
- x = 3
Linear equation solving: isolate the variable. Step 1: subtract 7 from both sides: 3x + 7 − 7 = 22 − 7, giving 3x = 15. Step 2: divide both sides by 3: 3x ÷ 3 = 15 ÷ 3, giving x = 5. Verify: 3(5) + 7 = 15 + 7 = 22 ✓. The two-step linear equation is the foundation of algebra. Strategy: undo operation… Full explanation →
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If 2(x − 4) = 14, what is the value of x?
Two approaches both work. Approach 1 — distribute first: 2(x − 4) = 14 becomes 2x − 8 = 14; add 8: 2x = 22; divide by 2: x = 11. Approach 2 — divide first: divide both sides by 2: x − 4 = 7; add 4: x = 11. Verify: 2(11 − 4) = 2(7) = 14 ✓. When the variable appears once inside parentheses with a coef… Full explanation →
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Simplify: 4(2x + 3) − 2(x − 5)
- 6x + 2
- 6x + 22 ✓
- 8x + 17
- 10x + 7
Distribute each coefficient through its parentheses, watching signs. 4(2x + 3) = 8x + 12. −2(x − 5) = −2x + 10 (note: −2 times −5 = +10). Combine: 8x + 12 − 2x + 10. Combine like terms: (8x − 2x) + (12 + 10) = 6x + 22. The most common error is sign mistakes when distributing a negative coefficient —… Full explanation →
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Solve the system: x + y = 10 and x − y = 4
- x = 3, y = 7
- x = 7, y = 3 ✓
- x = 6, y = 4
- x = 5, y = 5
System of two equations in two unknowns. Elimination method (often easiest for ASVAB): add the equations to eliminate y. (x + y) + (x − y) = 10 + 4, giving 2x = 14, so x = 7. Substitute back: 7 + y = 10, so y = 3. Verify both: 7 + 3 = 10 ✓ and 7 − 3 = 4 ✓. Substitution method: solve first equation f… Full explanation →
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What is the area of a rectangle with length 12 and width 8?
Area of a rectangle = length × width = 12 × 8 = 96 square units. Memorize basic geometry formulas: (1) Rectangle area = l × w, perimeter = 2(l + w); (2) Square area = s², perimeter = 4s; (3) Triangle area = ½ × base × height; (4) Circle area = πr², circumference = 2πr; (5) Parallelogram area = base … Full explanation →
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What is the area of a circle with radius 5?
Area of a circle = πr², where r is the radius. With r = 5: A = π(5)² = 25π square units. Numerically: 25π ≈ 25 × 3.14159 ≈ 78.5 square units. Common ASVAB answer choices keep π symbolic to avoid arithmetic ambiguity. Related circle formulas: (1) Diameter = 2r (twice the radius); (2) Circumference = … Full explanation →
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A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?
Pythagorean theorem: in a right triangle, a² + b² = c², where a and b are the legs and c is the hypotenuse (the longest side, opposite the right angle). Here: 3² + 4² = 9 + 16 = 25, so c² = 25, and c = √25 = 5. The 3-4-5 right triangle is a famous Pythagorean triple — memorize it and its multiples (… Full explanation →
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What is the volume of a rectangular box with length 5, width 4, and height 3?
Volume of a rectangular prism (box) = length × width × height = 5 × 4 × 3 = 60 cubic units. Multiply in any order: 5 × 4 = 20, then 20 × 3 = 60. Volume formulas to know: (1) Rectangular prism: V = lwh; (2) Cube: V = s³ (side cubed); (3) Cylinder: V = πr²h (area of circular base times height); (4) Co… Full explanation →
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What is 2⁵?
2⁵ means 2 multiplied by itself 5 times: 2 × 2 × 2 × 2 × 2 = 4 × 2 × 2 × 2 = 8 × 2 × 2 = 16 × 2 = 32. Memorize common powers: 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024. Also: 3² = 9, 3³ = 27, 3⁴ = 81; 4² = 16, 4³ = 64; 5² = 25, 5³ = 125. Expo… Full explanation →
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Simplify: √48
Simplify radicals by finding perfect-square factors. Factor 48: 48 = 16 × 3, where 16 is a perfect square. So √48 = √(16 × 3) = √16 × √3 = 4√3. The perfect-square factor comes out of the radical; the remaining factor stays inside. Steps: (1) Find the largest perfect-square factor; (2) Rewrite as a p… Full explanation →
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What is x⁻² when x = 4?
Negative exponents indicate reciprocals: a^(−n) = 1/a^n. So x⁻² = 1/x². With x = 4: x⁻² = 1/4² = 1/16. The negative exponent does NOT make the result negative — it makes it a reciprocal. Negative exponent rules: (1) a^(−n) = 1/a^n; (2) (a/b)^(−n) = (b/a)^n (flip the fraction, change sign); (3) 1/a^(… Full explanation →
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Factor: x² + 7x + 12
- (x − 3)(x − 4)
- (x + 3)(x + 4) ✓
- (x + 1)(x + 12)
- (x + 2)(x + 6)
Factoring a trinomial x² + bx + c: find two numbers that multiply to c and add to b. Here: multiply to 12, add to 7. Try pairs: 1 × 12 = 12, but 1 + 12 = 13 ✗; 2 × 6 = 12, but 2 + 6 = 8 ✗; 3 × 4 = 12, and 3 + 4 = 7 ✓. So x² + 7x + 12 = (x + 3)(x + 4). Verify by FOIL (First, Outer, Inner, Last): (x +… Full explanation →
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Factor: x² − 16
- (x − 4)(x − 4)
- (x + 8)(x − 2)
- (x + 4)(x − 4) ✓
- Cannot be factored
Difference of squares pattern: a² − b² = (a + b)(a − b). Here x² − 16 = x² − 4², so a = x and b = 4. Factored: (x + 4)(x − 4). Verify by FOIL: (x + 4)(x − 4) = x² − 4x + 4x − 16 = x² − 16 ✓. The middle terms cancel because of the +/− pattern. Key pattern recognition: a² − b² (difference) factors eas… Full explanation →
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Solve: x² − 5x + 6 = 0
- x = 5, x = 6
- x = −2, x = −3
- x = 2, x = 3 ✓
- x = 1, x = 6
Solve quadratic equations by factoring when possible. Step 1: factor — find numbers that multiply to 6 and add to −5: that's −2 and −3 (since (−2)(−3) = 6 and −2 + −3 = −5). So x² − 5x + 6 = (x − 2)(x − 3). Step 2: set the factored form equal to zero: (x − 2)(x − 3) = 0. Step 3: zero-product propert… Full explanation →
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What is the prime factorization of 60?
- 2 × 30
- 2² × 3 × 5 ✓
- 6 × 10
- 4 × 15
Prime factorization expresses a number as a product of prime numbers. Process: divide by smallest primes repeatedly. 60 ÷ 2 = 30; 30 ÷ 2 = 15; 15 ÷ 3 = 5; 5 ÷ 5 = 1. So 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5. Primes are natural numbers > 1 divisible only by 1 and themselves: 2, 3, 5, 7, 11, 13, 17, 19, 23,… Full explanation →
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What is the greatest common factor (GCF) of 24 and 36?
GCF (greatest common factor) is the largest number that divides both. Method 1 — prime factorization: 24 = 2³ × 3; 36 = 2² × 3². Common prime factors with smallest exponents: 2² (smaller of 2³ and 2²) and 3¹ (smaller of 3¹ and 3²). GCF = 2² × 3 = 4 × 3 = 12. Method 2 — list factors: factors of 24: 1… Full explanation →
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What is the sum of interior angles of a triangle?
The sum of interior angles of any triangle is always 180°. This is a fundamental geometric fact. Other polygon angle sums: (1) Quadrilateral: 360°; (2) Pentagon: 540°; (3) Hexagon: 720°; (4) n-gon: (n − 2) × 180°. For regular polygons (all sides and angles equal): each interior angle = (n − 2) × 180… Full explanation →
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If 4y − 9 = 11, what is y?
Two-step linear equation. Add 9 to both sides: 4y − 9 + 9 = 11 + 9, giving 4y = 20. Divide both sides by 4: 4y ÷ 4 = 20 ÷ 4, giving y = 5. Verify: 4(5) − 9 = 20 − 9 = 11 ✓. The algorithm: undo operations in reverse order of operations. The original expression performs (1) multiply variable by 4, the… Full explanation →
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Two angles are supplementary. If one is 75°, what is the other?
Supplementary angles sum to 180°. So the other angle = 180° − 75° = 105°. Angle relationships to know: (1) Complementary — sum to 90° (think 'right angle'); (2) Supplementary — sum to 180° (think 'straight angle'); (3) Vertical (vertically opposite) — formed by intersecting lines; vertical angles ar… Full explanation →
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Simplify: (3x²)(4x³)
Multiply coefficients and apply exponent rules to variables. Coefficients: 3 × 4 = 12. Variables: x² × x³ — use the product rule a^m × a^n = a^(m+n), so x² × x³ = x^(2+3) = x⁵. Combined: 12x⁵. Common error: multiplying exponents instead of adding (multiplication of like bases ADDS exponents; raising… Full explanation →
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What is the circumference of a circle with diameter 14? (Use π ≈ 22/7)
Circumference = πd = (22/7) × 14 = (22 × 14)/7 = 22 × 2 = 44 units. Or use 2πr with radius = 7: C = 2π(7) = 14π = 14 × (22/7) = 44. Circle formulas: (1) Diameter = 2 × radius, so radius = diameter/2; (2) Circumference C = πd = 2πr (length around the circle); (3) Area = πr² (surface inside); (4) The … Full explanation →
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What is 30% of 80?
Percent means 'per hundred'; convert to a decimal or fraction and multiply. 30% = 0.30 = 30/100 = 3/10. So 30% of 80 = 0.30 × 80 = 24. Or use fraction: (3/10) × 80 = 240/10 = 24. Percent applications: (1) Tax: total = price × (1 + tax rate); (2) Discount: sale price = original × (1 − discount rate);… Full explanation →
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Solve the inequality: 2x − 5 > 7
- x < 6
- x > 12
- x > 6 ✓
- x > 1
Solve inequalities like equations, but reverse the inequality sign when multiplying or dividing by a negative. Step 1: add 5: 2x > 12. Step 2: divide by 2 (positive, so don't flip): x > 6. Verify: try x = 7: 2(7) − 5 = 9 > 7 ✓; try x = 5: 2(5) − 5 = 5, not > 7 ✗. Inequality symbols: (1) > greater th… Full explanation →
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A square has perimeter 36. What is its area?
Square: all four sides equal. Perimeter = 4 × side, so 36 = 4s, giving s = 9. Area = s² = 9² = 81 square units. Square properties to know: (1) All sides equal; (2) All angles 90°; (3) Diagonals are equal in length and bisect each other at 90°; (4) Diagonal length = s√2 (Pythagorean theorem with two … Full explanation →
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Simplify: (x² − 9) / (x − 3), assuming x ≠ 3
Factor and cancel. Numerator: x² − 9 = (x + 3)(x − 3) (difference of squares). Denominator: x − 3. Rewrite: [(x + 3)(x − 3)] / (x − 3). Cancel the (x − 3) factor: x + 3. The simplification is valid for x ≠ 3 (because at x = 3, the original expression has 0/0, undefined). For all other values of x, (… Full explanation →
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Solve for x: 3x + 9 = 24
3x = 24 - 9 = 15. x = 15 ÷ 3 = 5. Two-step linear equation: undo the addition first (subtract 9 from both sides), then undo the multiplication (divide both sides by 3). Check by substituting back: 3(5) + 9 = 15 + 9 = 24 ✓. The distractors come from slipping a step — 4 and 6 come from dividing 24 by … Full explanation →
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What is 4³?
4³ = 4 × 4 × 4 = 16 × 4 = 64. Exponents represent repeated multiplication. 4³ means 4 multiplied by itself 3 times, giving 64. Full explanation →
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Factor: x² - 9
- (x+3)(x+3)
- (x-3)(x+3) ✓
- (x-3)(x-3)
- (x-9)(x+1)
Difference of squares: a² - b² = (a-b)(a+b). Here: x² - 9 = x² - 3² = (x-3)(x+3). Recognise the pattern: a square term minus a perfect-square constant with no middle term is always a difference of squares. The distractors fail when expanded: (x − 3)(x − 3) = x² − 6x + 9 and (x + 3)(x + 3) = x² + 6x … Full explanation →
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Two angles of a triangle measure 65° and 75°. What is the third angle?
Sum of angles in a triangle = 180°. Third angle = 180° - 65° - 75° = 40°. The three interior angles of any triangle always total 180°, so once two are known the third is forced. Add the known angles first (65 + 75 = 140), then subtract from 180. A sanity check: 65°, 75° and 40° are all less than 90°… Full explanation →
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If f(x) = 2x - 3, what is f(7)?
f(7) = 2(7) - 3 = 14 - 3 = 11. Function notation f(7) just means 'replace every x in the rule with 7, then evaluate'. Follow order of operations: multiply first (2 × 7 = 14), then subtract 3. The distractor 17 adds 3 instead of subtracting; 8 is 7 + 1 or 2 × 7 − 6; 13 would be f(8). Writing the subs… Full explanation →
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What is the perimeter of a square with side length 9?
Perimeter of square = 4 × side = 4 × 9 = 36. Perimeter is the distance around a shape — for a square, four equal sides, so 4 × 9. The distractor 81 is the area (9 × 9), the most common mix-up; 18 is two sides (9 + 9), and 27 is three sides. Units confirm which you have: perimeter is in plain units (… Full explanation →
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Solve: 2(x + 4) = 22
Distribute: 2x + 8 = 22. Subtract 8: 2x = 14. Divide by 2: x = 7. Either distribute first, as shown, or divide both sides by 2 straight away: x + 4 = 11, so x = 7 — the second route is quicker when the number outside the bracket divides the other side evenly. Check: 2(7 + 4) = 2 × 11 = 22 ✓. The dis… Full explanation →
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Which of the following is a prime number?
37 is prime — only divisible by 1 and 37. 21 = 3×7; 27 = 3×9; 51 = 3×17. A prime has exactly two factors, 1 and itself. To test an odd number, try dividing by the small primes (3, 5, 7) up to its square root: 37 is not divisible by 3 (3 + 7 = 10, not a multiple of 3), does not end in 0 or 5, and 7 ×… Full explanation →
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A right triangle has legs of 5 and 12. What is the hypotenuse?
Pythagorean theorem: c² = a² + b² = 25 + 144 = 169. c = √169 = 13. 5-12-13 is one of the Pythagorean triples worth memorising, alongside 3-4-5 and 8-15-17 — the ASVAB uses them often because the square roots come out whole. The hypotenuse is always the longest side, opposite the right angle, so an a… Full explanation →
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What is the slope of the line passing through (2, 3) and (6, 11)?
Slope = (y₂-y₁)/(x₂-x₁) = (11-3)/(6-2) = 8/4 = 2. Slope is rise over run: the change in y divided by the change in x between any two points on the line. Keep the subtraction order consistent in both numerator and denominator ((11 − 3) over (6 − 2)); reversing only one of them gives −2, the wrong sig… Full explanation →
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Simplify: x³ × x⁴
When multiplying same base, add exponents: x³ × x⁴ = x^(3+4) = x⁷. Exponent rules: when multiplying powers with the same base, add the exponents; when raising a power to a power, multiply them; when dividing, subtract. The distractor x¹² multiplies the exponents (that would be (x³)⁴), 2x⁷ wrongly ad… Full explanation →
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The angles of a quadrilateral sum to how many degrees?
A quadrilateral (4 sides) has interior angles summing to 360°. Triangles sum to 180°; each additional side adds 180°. You can see why by splitting any quadrilateral along a diagonal into two triangles, each contributing 180°. The general formula is (n − 2) × 180° for an n-sided polygon: triangle 180… Full explanation →
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Solve the inequality: 2x - 5 > 9
- x > 7 ✓
- x > 6
- x > 2
- x > 4
Add 5 to both sides: 2x > 14. Divide by 2: x > 7. Solve an inequality exactly like an equation, with one exception: if you multiply or divide both sides by a negative number, flip the inequality sign. Here you divide by positive 2, so the sign stays as '>'. Check with a value: x = 8 gives 2(8) − 5 =… Full explanation →
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What is the least common multiple (LCM) of 4 and 6?
Multiples of 4: 4, 8, 12... Multiples of 6: 6, 12... First common multiple = 12. The LCM is the smallest number that both divide into evenly. Listing multiples works for small numbers; for larger ones, use prime factors — 4 = 2² and 6 = 2 × 3, so the LCM takes the highest power of each prime: 2² × 3… Full explanation →
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What is the area of a triangle with a base of 10 cm and a height of 6 cm?
- 30 cm² ✓
- 16 cm²
- 60 cm²
- 32 cm²
AREA of a triangle = ½ × base × height = ½ × 10 × 6 = ½ × 60 = 30 cm². ASVAB Mathematics Knowledge tests area formulas. Strategy: memorize the triangle area formula (½ × base × height) — a common error is forgetting the ½ and getting 60 (which is the area of a rectangle with those dimensions). The t… Full explanation →
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What is the value of 2⁵ (2 to the 5th power)?
2⁵ means 2 multiplied by itself 5 times: 2 × 2 × 2 × 2 × 2 = 32. ASVAB Mathematics Knowledge tests exponents. Work step by step: 2×2=4, ×2=8, ×2=16, ×2=32. COMMON ERROR: confusing 2⁵ with 2 × 5 = 10 — an exponent means repeated MULTIPLICATION, not multiplying the base by the exponent. Powers of 2 to… Full explanation →
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A rectangle has a length of 12 inches and a width of 5 inches. What is its perimeter?
- 17 inches
- 34 inches ✓
- 24 inches
- 60 inches
PERIMETER of a rectangle = 2 × (length + width) = 2 × (12 + 5) = 2 × 17 = 34 inches. ASVAB Mathematics Knowledge tests perimeter vs area. Strategy: PERIMETER is the distance around (add all sides; for a rectangle, 2L + 2W); AREA is the space inside (L × W = 60 sq in here). COMMON ERROR: confusing pe… Full explanation →
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Simplify: 4(x + 3) − 2x
- 2x + 7
- 2x + 12 ✓
- 6x + 12
- 2x + 3
Use the DISTRIBUTIVE property: 4(x + 3) = 4x + 12. Then subtract 2x: 4x + 12 − 2x = 2x + 12. ASVAB Mathematics Knowledge tests simplifying expressions. Strategy: (1) distribute the 4 across the parentheses: 4·x + 4·3 = 4x + 12; (2) combine like terms: 4x − 2x = 2x, and keep the +12. Result: 2x + 12.… Full explanation →
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What is the area of a circle with a radius of 4 (use π ≈ 3.14)?
AREA of a circle = πr² = 3.14 × 4² = 3.14 × 16 = 50.24 square units. ASVAB Mathematics Knowledge tests circle formulas. Strategy: square the radius FIRST (4² = 16), then multiply by π. COMMON ERROR: multiplying π × r first then squaring, or confusing area (πr²) with circumference (2πr = 2 × 3.14 × 4… Full explanation →
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Evaluate: 6 + 3 × 4 − 2
Use ORDER OF OPERATIONS (PEMDAS): multiplication before addition/subtraction. 3 × 4 = 12 first. Then: 6 + 12 − 2 = 18 − 2 = 16. ASVAB Mathematics Knowledge tests order of operations. PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). COMMON… Full explanation →
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If x² = 49, what are the possible values of x?
- 24.5
- 7 only
- 7 and −7 ✓
- ±49
If x² = 49, then x = ±7 (both 7 AND −7), because 7² = 49 AND (−7)² = 49. ASVAB Mathematics Knowledge tests square roots and equations. KEY CONCEPT: when solving x² = a number, there are usually TWO solutions — a positive and a negative root — because squaring a negative number gives a positive resul… Full explanation →
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In a right triangle, if the two legs are 3 and 4, what is the length of the hypotenuse?
Use the PYTHAGOREAN THEOREM: a² + b² = c², where c is the hypotenuse. Here: 3² + 4² = c² → 9 + 16 = 25 = c². So c = √25 = 5. ASVAB Mathematics Knowledge tests the Pythagorean theorem. The 3-4-5 triangle is the most common 'Pythagorean triple' and appears frequently — worth memorizing (along with 5-1… Full explanation →
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Solve for x: 3x − 7 = 14.
- x = 21
- x = 2.3
- x = 7 ✓
- x = 3
To solve a linear equation, isolate x. Start with 3x − 7 = 14. Add 7 to both sides: 3x = 21. Then divide both sides by 3: x = 7. The strategy is to undo operations in reverse order — first undo the subtraction (add 7), then undo the multiplication (divide by 3). You can check by substituting back: 3… Full explanation →
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Simplify: 2³ × 2⁴.
When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷. This is the product rule for exponents. Do not multiply the exponents (that rule applies to a power raised to a power) and do not change the base. So 2⁷ = 128 if you compute it out, but in simplified exponential f… Full explanation →
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A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
Use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse. Here 6² + 8² = 36 + 64 = 100, so c = √100 = 10. The 6-8-10 triangle is a multiple of the common 3-4-5 right triangle, so recognizing that pattern gives the answer instantly. Be careful: 100 is c², not c — you must take the square … Full explanation →
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Factor the expression: x² + 5x + 6.
- (x + 1)(x + 6)
- (x + 5)(x + 1)
- (x − 2)(x − 3)
- (x + 2)(x + 3) ✓
To factor x² + 5x + 6, find two numbers that multiply to the constant (6) and add to the middle coefficient (5). Those numbers are 2 and 3, since 2 × 3 = 6 and 2 + 3 = 5. So the factors are (x + 2)(x + 3). You can verify by expanding: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6. ✓ The other opti… Full explanation →
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If 2(x + 3) = 16, what is the value of x?
First distribute or divide. Dividing both sides by 2: x + 3 = 8. Then subtract 3: x = 5. Alternatively, distribute first: 2x + 6 = 16, then 2x = 10, so x = 5. Either order works. Check: 2(5 + 3) = 2(8) = 16. ✓ Equations with parentheses can be solved by distributing the multiplier or by dividing bot… Full explanation →
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What is √144?
The square root of 144 is the number that, multiplied by itself, gives 144. Since 12 × 12 = 144, √144 = 12. Memorizing perfect squares up to at least 15² (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225) makes these instant. The distractor 72 is 144 ÷ 2, a common error of halving inste… Full explanation →
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What is the perimeter of a rectangle with length 9 and width 4?
The perimeter of a rectangle is 2 × (length + width), or 2L + 2W. Here perimeter = 2 × (9 + 4) = 2 × 13 = 26. The distractor 36 is the area (9 × 4), so don't confuse perimeter (distance around) with area (space inside). The perimeter is 26 units. A reliable approach is to add the length and width, t… Full explanation →
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Solve the inequality: x + 5 > 12.
- x > 17
- x > 7 ✓
- x < 7
- x > 5
Solve an inequality much like an equation: subtract 5 from both sides of x + 5 > 12 to get x > 7. The solution is all values greater than 7. Note that the inequality sign stays the same when adding or subtracting; it only flips when you multiply or divide both sides by a negative number (which doesn… Full explanation →
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What is the circumference of a circle with a diameter of 10? (Use π ≈ 3.14)
Circumference is π × diameter (C = πd), or equivalently 2πr. With a diameter of 10: C = 3.14 × 10 = 31.4. Be careful not to use the area formula (πr²); the area here would be 3.14 × 5² = 78.5, offered as a distractor. Since the diameter is given directly, C = πd is the fastest route. The circumferen… Full explanation →
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Simplify the expression: 3(2x + 4) − 2x.
- 6x + 4
- 8x + 12
- 4x + 4
- 4x + 12 ✓
First distribute the 3 across the parentheses: 3 × 2x = 6x and 3 × 4 = 12, giving 6x + 12. Then subtract 2x: 6x + 12 − 2x. Combine like terms (6x − 2x = 4x): the result is 4x + 12. The key steps are distributing first, then combining like terms (the x-terms together, the constants separately). A com… Full explanation →
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What is 30% expressed as a fraction in lowest terms?
A percent means 'per hundred,' so 30% = 30/100. Reduce by dividing the numerator and denominator by their greatest common factor, 10: 30/100 = 3/10. The fraction in lowest terms is 3/10. The distractor 3/100 omits the reduction step incorrectly (it confuses 30/100 reduction), and 1/3 is a different … Full explanation →
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Simplify: (3²)³.
When raising a power to another power, multiply the exponents: (3²)³ = 3^(2×3) = 3⁶. This is the power-of-a-power rule, distinct from the product rule (where you add exponents for multiplication of like bases). So (3²)³ = 3⁶, which equals 729 if computed out. The common mistake is adding the exponen… Full explanation →