Practice Powers and roots
Powers describe repeated multiplication, while roots reverse a power when defined.
These operations help you work with areas, growth and very large or small numbers.
Exercises with solutions
To multiply powers with the same base, add the exponents; to divide them, subtract the exponents. A negative exponent means the reciprocal. A root is a power with a fractional exponent.
Exercise 1
Write as a single power: 3⁴ · 3².
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3⁶
With the same base the exponents are added: 4 + 2 = 6.
Exercise 2
Calculate 2⁻³.
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1/8
A negative exponent means the reciprocal: 2⁻³ = 1 ÷ 2³ = 1/8.
Exercise 3
Write √7 as a power.
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7 to the power 1/2
The nth root is the power with exponent 1/n. For a square root n = 2.
Exercise 4
Calculate (2³)².
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64
For a power of a power the exponents are multiplied: 3 · 2 = 6, so 2⁶ = 64.
Common mistake
Adding exponents in a sum. 2³ + 2² is not 2⁵ but 8 + 4 = 12. The rule only applies to products with the same base.
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