#separator:tab #html:false #tags column:4 Product rule aᵐ · aⁿ = aᵐ⁺ⁿ (Same base: add exponents) math-exponent-rules Quotient rule aᵐ / aⁿ = aᵐ⁻ⁿ (Same base: subtract exponents) math-exponent-rules Power of a power (aᵐ)ⁿ = aᵐⁿ (Multiply exponents) math-exponent-rules Power of a product (ab)ⁿ = aⁿbⁿ math-exponent-rules Power of a quotient (a/b)ⁿ = aⁿ/bⁿ math-exponent-rules Zero exponent a⁰ = 1, for a not zero math-exponent-rules Negative exponent a⁻ⁿ = 1/aⁿ math-exponent-rules Fractional exponent a^(1/n) = the nth root of a math-exponent-rules Rational exponent a^(m/n) = (nth root of a)^m math-exponent-rules Exponent of 1 a¹ = a math-exponent-rules 2³ · 2⁴ 2⁷ = 128 math-exponent-rules 5⁶ / 5² 5⁴ = 625 math-exponent-rules (3²)³ 3⁶ = 729 math-exponent-rules (2x)³ 8x³ math-exponent-rules (x²)⁴ x⁸ math-exponent-rules x³ · x⁵ x⁸ math-exponent-rules x⁹ / x³ x⁶ math-exponent-rules (−2)² 4 math-exponent-rules −2² −4 (The exponent applies only to the 2) math-exponent-rules (−2)³ −8 math-exponent-rules 10⁰ 1 math-exponent-rules 0⁰ Usually left undefined (or treated as 1 in some settings) math-exponent-rules 2⁻³ 1/8 math-exponent-rules 10⁻² 0.01 math-exponent-rules 4^(1/2) 2 math-exponent-rules 8^(1/3) 2 math-exponent-rules 27^(2/3) 9 math-exponent-rules 16^(3/4) 8 math-exponent-rules 9^(−1/2) 1/3 math-exponent-rules Is (a + b)² equal to a² + b²? No. (a + b)² = a² + 2ab + b² math-exponent-rules Is aᵐ + aⁿ = aᵐ⁺ⁿ? No. The product rule works for multiplying, not adding math-exponent-rules Negative base with even power The result is positive math-exponent-rules Negative base with odd power The result is negative math-exponent-rules Scientific notation of 45,000 4.5 × 10⁴ math-exponent-rules Scientific notation of 0.0007 7 × 10⁻⁴ math-exponent-rules (3 × 10²)(2 × 10³) 6 × 10⁵ math-exponent-rules Square root as an exponent √a = a^(1/2) math-exponent-rules Cube root as an exponent ∛a = a^(1/3) math-exponent-rules Reciprocal of x⁻² x² math-exponent-rules Simplify (x³y²)² x⁶y⁴ math-exponent-rules Simplify x⁻²y³ with positive exponents y³/x² math-exponent-rules