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

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