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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.

Maine Learning Results 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 Maine

In the Maine Learning Results, 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: Maine 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 4³ ÷ 4².

    • 4⁵
    • 1¹
    • 4²
    • 4¹

  2. Question 2

    Simplify (6⁴)².

    • 6⁶
    • 6⁹
    • 12⁴
    • 6⁸

  3. Question 3

    What is 4⁻³?

    • −64
    • 64
    • −1/64
    • 1/64

  4. Question 4

    What is the value of 3⁴ × 3⁻²?

    • 9
    • 81
    • 729
    • 27

  5. Question 5

    Simplify 6³ × 6⁷.

    • 6²¹
    • 6⁴
    • 6¹⁰
    • 36¹⁰

  6. Question 6

    Simplify 9⁷ ÷ 9⁵.

    • 9²
    • 9¹
    • 1²
    • 9¹²

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