Subscribe

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.

Alaska content standards learning standard: 8.EE.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 Alaska

In the Alaska content 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: Alaska Department of Education and Early Development

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

    What is 3⁻¹?

    • 3
    • −3
    • 1/3
    • −1/3

  2. Question 2

    What is the value of 5³ × 5⁻²?

    • 125
    • 3125
    • 25
    • 5

  3. Question 3

    Simplify 3⁵ × 3⁶.

    • 3¹¹
    • 3³⁰
    • 9¹¹
    • 3¹

  4. Question 4

    Simplify 7⁹ ÷ 7⁶.

    • 7¹⁵
    • 7³
    • 7²
    • 1³

  5. Question 5

    Simplify (3⁴)⁵.

    • 3²¹
    • 3²⁰
    • 15⁴
    • 3⁹

  6. Question 6

    Simplify (8³)².

    • 8⁵
    • 16³
    • 8⁷
    • 8⁶

More 8th grade