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Exponents and radicals practice

Multiplying powers worksheets

Practice 14 products of powers with numeric, fractional and variable bases. Choose positive exponents or mixed signs and write simplified positive-exponent answers.

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Combine matching bases and write answers with positive exponents. Keep any nonzero restrictions stated for the original expression.

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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

Combine powers with the same base by adding their exponents while preserving any original domain restrictions.

Worked example

Simplify x⁴ × x⁻⁶ for x ≠ 0.

1/x², with x ≠ 0.

Add 4 and −6 to get −2. Rewrite x⁻² as 1/x². The original negative power already excludes zero.

Teaching notes

Make the practice count

  • Circle equal bases before combining exponents.
  • Keep unlike bases separate.
  • Use a number line if signed exponent addition is the obstacle.
  • Read the final expression and its domain together.

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Math SheetNameScore/ 14TeacherDateMultiply PowersCombine like bases and write positive exponents.1.42·4-42.47-6·473·47-23.y2·y-2Domain: real variablesyRy04.9-1·95·9-45.132·13-16.x-3·x·x-1Domain: real variablesxRx07.52·5-48.16-3·16·16-49.y·y-5Domain: real variablesyRy010.2-4·23·2-111.122·12-612.x-4·x·x-4Domain: real variablesxRx0math-sheet.comPage 1 / 2
Math SheetNameScore/ 14TeacherDateMultiply PowersCombine like bases and write positive exponents.13.7·7-614.56-4·562·56-6math-sheet.comPage 2 / 2

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