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8th grade · Math · Unit 12 of 17

Exponent Rules

Add, subtract, multiply exponents

What your child practices

Properties of integer exponents: multiplying and dividing powers with the same base, a power of a power, zero exponents and negative exponents.

Arizona Academic Standards learning standard: 8.EE.A.1 · applying the properties of integer exponents to write equivalent expressions

How we explain it

Children can open this short lesson before they practice.

  1. Multiply powers with the same base: add the exponents.
  2. Divide: subtract the exponents. Power of a power: multiply them.
  3. a⁰ = 1, and a⁻ⁿ = 1/aⁿ.

Example: Simplify 2³ × 2⁴. Same base, so add: 3 + 4 = 7. Answer: 2⁷

Exponent Rules in Arizona

In the Arizona Academic Standards, this is unit 12 of 17 in 8th grade Math, after Congruent Shapes and before Systems of Equations.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Arizona Department of Education

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Simplify 8⁵ ÷ 8⁴.

    • 8¹
    • 8²⁰
    • 1¹
    • 8⁹

  2. Question 2

    Simplify (3⁵)³.

    • 3¹⁶
    • 3⁸
    • 9⁵
    • 3¹⁵

  3. Question 3

    What is 3⁻³?

    • −27
    • −1/27
    • 27
    • 1/27

  4. Question 4

    What is the value of 2³ × 2⁻¹?

    • 4
    • 8
    • 7
    • 16

  5. Question 5

    Simplify 9⁵ × 9⁴.

    • 9⁹
    • 81⁹
    • 9¹
    • 9²⁰

  6. Question 6

    What is 5⁻¹?

    • −1/5
    • −5
    • 5
    • 1/5

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