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Exponents and radicals practice

Mixed exponent rules worksheets

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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Simplify using the law that matches each operation. Finish with positive exponents and keep the original domain restrictions.

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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.

The preview and downloaded PDF use the same resolved questions. Answers follow on separate pages; choose the student-only edition when handing out the exercise.

Learning objective

What this activity builds

Identify and combine exponent laws across a varied set of numeric and algebraic expressions.

Worked example

Simplify (2x⁻²)³ × x⁵ for x ≠ 0.

8/x, with x ≠ 0.

The outer cube gives 8x⁻⁶. Multiplying by x⁵ gives 8x⁻¹, which is 8/x.

Teaching notes

Make the practice count

  • Use the reference sheet to name each step.
  • Simplify powers inside or around groups before combining like bases.
  • Select two rules at a time before adding the full mix.
  • Check results using a nonzero substitution after the algebra is complete.

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Math SheetNameScore/ 12TeacherDateMixed Exponent OperationsUse the indicated exponent law and write positive exponents.1.82·8-22.59-45933.6·y6·z-15Domain: real variablesz04.3·x-45·z24Domain: real variablesx0z05.372·37-16.x-1x5Domain: real variablesxRx07.358.4·x-39·z42Domain: real variablesx0z09.y4·y-2Domain: real variablesyRy010.4-44math-sheet.comPage 1 / 2
Math SheetNameScore/ 12TeacherDateMixed Exponent OperationsUse the indicated exponent law and write positive exponents.11.9·y5512.3·x-13·z3Domain: real variablesx0z0math-sheet.comPage 2 / 2

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