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.
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Evaluate powers of integer bases worksheets
Choose positive, negative, zero, unit or fractional exponents for 20 integer-base problems. Practice exact real-number values with independently selected base signs.
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Evaluate each expression in the real numbers. For a fractional exponent, find the indicated root; for a negative exponent, take the reciprocal.
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Choose one challenge at a time
Start with a focused choice of operations or expression types. Combine them when the learner can explain the rule being used, as well as calculate the result.
Read the domain printed on variable problems. A simplified expression must keep any values excluded by the original denominator or radical.
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Learning objective
What this activity builds
Interpret integer and rational exponents as repeated powers, reciprocals and roots of integer bases.
Worked example
Evaluate 81 to the power −1/4.
1/3.
The principal fourth root of 81 is 3. The minus sign in the exponent makes the result its reciprocal.
Teaching notes
Make the practice count
- Practice exponent kinds separately before mixing them.
- Compare exponent zero, exponent one and exponent negative one.
- Use perfect-power bases to keep rational-exponent results exact.
- For a negative base, discuss why an even-index real root is unavailable.
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