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Exponent laws practice

A few exponent rules cover almost everything: same base means add, subtract or multiply the exponents.

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How it works

RuleExample
am × an = am+n2² × 2⁴ = 2⁶
am ÷ an = am−n5⁷ ÷ 5⁴ = 5³
(am)n = amn(x⁴)⁴ = x¹⁶
(ab)n = anbn(2x)⁴ = 16x⁴
a⁰ = 1, a−n = 1/anx⁻² = 1/x²

To solve exponential equations, write both sides as powers of the same base and set the exponents equal: 729 = 3⁶, so 32x = 729 means 2x = 6. It helps to know the powers of 2 up to 2¹⁰ = 1024 and the powers of 3 up to 3⁶ = 729.

Exponent laws practice problems with solutions

These problems come from Mathyessy's question bank. Try each one before opening the solution.

  1. Simplify 22 × 24.

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    Answer: 64

    Same base, so add the exponents: 2² × 2⁴ = 2⁶ = 64.

  2. Simplify (2x4)4. What is the coefficient?

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    Answer: 16

    Raise each factor to the 4th power: 2⁴ × (x⁴)⁴ = 16x¹⁶. The coefficient is 16.

  3. Simplify x5 × x-2 × x3. Give the exponent of the simplified xn form.

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    Answer: 6

    Add the exponents: 5 + (−2) + 3 = 6, giving x⁶.

  4. If 32x = 729, what is x?

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    Answer: 3

    729 = 3⁶, so 2x = 6 and x = 3.

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