Exponents and radicals
Multiplying and dividing powers worksheets
Choose multiplication, division or a balanced mix for 12 exponent-law problems. Use positive or mixed signed exponents with exact simplified answers.
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Dividing powers worksheets
Generate 12 quotients of powers with positive or mixed signed exponents. Simplify coefficients and variable powers while retaining restrictions from denominators and negative powers.
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Simplify each quotient. State the result with positive exponents and retain all exclusions from the original expression, including denominators and negative powers.
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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
Subtract denominator exponents from numerator exponents and rewrite negative powers across the fraction bar.
Worked example
Simplify x³/x⁷ for x ≠ 0.
1/x⁴, with x ≠ 0.
Subtract 7 from 3 to obtain x⁻⁴. The equivalent reciprocal is 1/x⁴, and zero remains excluded.
Teaching notes
Make the practice count
- Write numerator exponent minus denominator exponent in that order.
- Handle coefficients separately from variable powers.
- Check subtraction carefully when the denominator exponent is negative.
- Keep a canceled variable in the domain restrictions.
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Combine multiplication, division, powers of products and powers of quotients in 12 questions. Select the operations and positive, negative or mixed exponents.
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