Practice Exponents in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An operation representing repeated multiplication: ana^n means aa multiplied by itself nn times. For example, 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8. Exponents extend to zero, negative, and fractional powers.

232^3 means 2×2×2=82 \times 2 \times 2 = 8. The exponent tells you how many times to multiply.

Showing a random 20 of 50 problems.

Example 1

easy
Compute 262^6.

Example 2

hard
Solve for xx: 2x=322^x = 32.

Example 3

hard
Solve 3x+1=813^{x+1} = 81.

Example 4

easy
Compute (32)3(3^2)^3.

Example 5

medium
Compute 6764\frac{6^7}{6^4}.

Example 6

medium
Compute 91/29^{1/2}.

Example 7

easy
Compute 626^2.

Example 8

easy
Compute 10410^4.

Example 9

medium
Simplify (x3)4(x^3)^4.

Example 10

easy
Compute 42⋅434^2 \cdot 4^3 as a power of 44.

Example 11

medium
Express 0.0010.001 as a power of 1010.

Example 12

easy
Compute 535^3.

Example 13

easy
Compute 343^4.

Example 14

medium
Compute (12)4\left(\tfrac{1}{2}\right)^4.

Example 15

hard
Which is larger, 2102^{10} or 10310^3?

Example 16

easy
Compute 505^0.

Example 17

hard
Simplify 82/38^{2/3}.

Example 18

challenge
Simplify (x2y−3)−2x−1y4\frac{(x^2 y^{-3})^{-2}}{x^{-1} y^4}.

Example 19

medium
Simplify 25×2324\frac{2^5 \times 2^3}{2^4}.

Example 20

challenge
If 2x=322^x = 32, find xx.
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