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Exponents and radicals reference

Exponent rules reference sheet

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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Reference · LetterReference · A4
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Read each rule with its example and restrictions. Keep the sheet nearby while simplifying powers.

Download the complete reference with its explanations and worked examples. This handout does not need a separate answer key.

US Letter

Reference handout

A4

Reference handout
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A reference to use alongside practice

The reference brings eight exponent laws together with examples and the conditions under which they apply. The preview shows the first page; download the PDF for the complete reference.

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Learning objective

What this activity builds

Choose an exponent law from the structure of an expression and check that its bases satisfy the stated conditions.

Worked example

Why is 7³ × 7² equal to 7⁵?

The product contains five factors of 7.

The first power supplies three factors and the second supplies two. Add the exponents because the bases match and the powers are being multiplied.

Teaching notes

Make the practice count

  • Ask the learner to name the operation before choosing a law.
  • Use a repeated product to explain a rule before using symbols.
  • Check nonzero-base conditions for zero or negative exponents.
  • Connect fractional exponents to roots and their real-number domains.

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2 reference pages
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Math SheetNameScoreTeacherDateExponent Rules ReferenceUse each law with its stated domain condition.a01Domain: real variablesa0A nonzero base to the zero power is one.701a-m1amDomain: real variablesa0m: integersA negative exponent moves a nonzero power across the fraction bar.3-219am·anam+nDomain: real variablesa0m: integersn: integersMultiplying like bases adds exponents.23·2427amanam-nDomain: real variablesa0m: integersn: integersDividing like nonzero bases subtracts exponents.565254math-sheet.comPage 1 / 2
Math SheetNameScoreTeacherDateExponent Rules ReferenceUse each law with its stated domain condition.amnam·nDomain: real variablesa0m: integersn: integersA power of a power multiplies exponents.23226a·bmam·bmDomain: real variablesa0b0m: integersA power distributes to every product factor.2·3222·32abmambmDomain: real variablesa0b0m: integersA power distributes to numerator and nonzero denominator.23249apqqapDomain: real variablesa0q2p: integersq: integersA rational exponent combines a power with an indexed root.163264math-sheet.comPage 2 / 2

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