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^(−n) = a^n. Examples: 2⁻³ = 1/2³ = 1/8; (1/3)⁻² = 3² = 9; 10⁻⁴ = 0.0001. Zero exponent: a⁰ = 1 for any non-zero a. 0⁰ is undefined (or 1 by convention in some contexts). Fractional exponents: a^(1/n) = ⁿ√a; a^(m/n) = ⁿ√(a^m) = (ⁿ√a)^m. Example: 8^(2/3) = (³√8)² = 2² = 4. These rules combine: (1/2)⁻³ = 2³ = 8.