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Exponent Rules
The laws of exponents, with worked examples including zero, negative and fractional exponents.
0 of 41 known
41 cards
- Product ruleRuleaᵐ · aⁿ = aᵐ⁺ⁿSame base: add exponents
- Quotient ruleRuleaᵐ / aⁿ = aᵐ⁻ⁿSame base: subtract exponents
- Power of a powerRule(aᵐ)ⁿ = aᵐⁿMultiply exponents
- Power of a productRule(ab)ⁿ = aⁿbⁿ
- Power of a quotientRule(a/b)ⁿ = aⁿ/bⁿ
- Zero exponentRulea⁰ = 1, for a not zero
- Negative exponentRulea⁻ⁿ = 1/aⁿ
- Fractional exponentRulea^(1/n) = the nth root of a
- Rational exponentRulea^(m/n) = (nth root of a)^m
- Exponent of 1Rulea¹ = a
- 2³ · 2⁴Rule2⁷ = 128
- 5⁶ / 5²Rule5⁴ = 625
- (3²)³Rule3⁶ = 729
- (2x)³Rule8x³
- (x²)⁴Rulex⁸
- x³ · x⁵Rulex⁸
- x⁹ / x³Rulex⁶
- (−2)²Rule4
- −2²Rule−4The exponent applies only to the 2
- (−2)³Rule−8
- 10⁰Rule1
- 0⁰RuleUsually left undefined (or treated as 1 in some settings)
- 2⁻³Rule1/8
- 10⁻²Rule0.01
- 4^(1/2)Rule2
- 8^(1/3)Rule2
- 27^(2/3)Rule9
- 16^(3/4)Rule8
- 9^(−1/2)Rule1/3
- Is (a + b)² equal to a² + b²?RuleNo. (a + b)² = a² + 2ab + b²
- Is aᵐ + aⁿ = aᵐ⁺ⁿ?RuleNo. The product rule works for multiplying, not adding
- Negative base with even powerRuleThe result is positive
- Negative base with odd powerRuleThe result is negative
- Scientific notation of 45,000Rule4.5 × 10⁴
- Scientific notation of 0.0007Rule7 × 10⁻⁴
- (3 × 10²)(2 × 10³)Rule6 × 10⁵
- Square root as an exponentRule√a = a^(1/2)
- Cube root as an exponentRule∛a = a^(1/3)
- Reciprocal of x⁻²Rulex²
- Simplify (x³y²)²Rulex⁶y⁴
- Simplify x⁻²y³ with positive exponentsRuley³/x²
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