Exponents and radicals
Evaluate powers of fractions worksheets
Practice 20 powers with fraction bases and positive, negative, zero, unit or fractional exponents. Select base signs and print exact reduced answers.
Preview and downloadExponents and radicals practice
Solving rational exponent equations worksheets
Solve twelve exact rational exponent equations over the real numbers. Choose easy, medium or hard profiles and print a worked answer key with domain and substitution checks.
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Solve each equation over the real numbers. Reduce the exponent first, give all solutions and check every candidate in the original equation.
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The reduced exponent determines every real branch
Reduce the exponent before using its numerator and denominator. An even root restricts the affine base, while an odd root permits negative bases; every negative power also excludes a zero base.
The worked key isolates the power with exact fraction arithmetic, lists every permitted base branch, solves the affine equation and substitutes each result into the original equation.
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Learning objective
What this activity builds
Isolate a rational power, apply its reduced exponent and real-number domain, then give the complete exact solution set.
Worked example
Solve x^(2/3) = 4 over the real numbers.
x = -8 or x = 8.
The cube-root base may be negative. Squaring it gives 4 for both cube-root values -2 and 2, so both original values work.
Teaching notes
Make the practice count
- Reduce the rational exponent before deciding the domain.
- An even root requires a nonnegative base, and a negative exponent also excludes zero.
- Keep both branches when an even numerator and odd denominator allow them.
- Substitute every candidate into the original equation.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one or more profiles for twelve equations. Solve over the real numbers, keep every valid branch, and check each answer in the original equation.
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A useful next step
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