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. Exponent rules: (1) a^m · a^n = a^(m+n); (2) a^m / a^n = a^(m−n); (3) (a^m)^n = a^(m·n); (4) a⁰ = 1 (for a ≠ 0); (5) a^(−n) = 1/a^n; (6) a^(1/n) = ⁿ√a (the n-th root); (7) (ab)^n = a^n · b^n; (8) (a/b)^n = a^n / b^n. Common error: 2⁵ ≠ 2 × 5 = 10. Exponents are repeated multiplication, not multiplication.