Exponents and radicals
Powers of quotients worksheets
Generate 12 powers of numeric and algebraic quotients. Apply the exponent to numerator and denominator, reduce the result and preserve excluded values.
Preview and downloadExponents and radicals practice
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 the power of the whole parenthesized fraction. Simplify the final numerator and denominator and keep the denominator positive.
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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
Apply a power to both parts of a fraction and handle reciprocals and exact roots consistently.
Worked example
Evaluate (4/9) to the power −1/2.
3/2.
The principal square root of 4/9 is 2/3. Its reciprocal is 3/2.
Teaching notes
Make the practice count
- Mark the numerator and denominator as parts of one base.
- Raise both parts to the exponent.
- For a negative power, invert the fraction before or after evaluating.
- Check the sign using the base and the parity of an integer exponent.
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Print an exponent rules reference with original examples of zero, negative and rational exponents, products, quotients and powers. Includes the conditions each rule needs.
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