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8th grade · Math · Unit 13 of 19

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.

New York State Learning Standards learning standard: NY-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 New York

In the New York State Learning Standards, this is unit 13 of 19 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: New York State Education Department (NYSED)

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 4⁻¹?

    • 1/4
    • −1/4
    • −4
    • 4

  2. Question 2

    Simplify (6⁴)⁴.

    • 6¹⁷
    • 24⁴
    • 6¹⁶
    • 6⁸

  3. Question 3

    Simplify 6⁵ ÷ 6².

    • 6³
    • 6⁷
    • 6¹⁰
    • 1³

  4. Question 4

    Simplify 2³ × 2⁹.

    • 2¹²
    • 2²⁷
    • 2⁶
    • 4¹²

  5. Question 5

    What is the value of 3² × 3⁻¹?

    • 9
    • 27
    • 1
    • 3

  6. Question 6

    What is 10⁻²?

    • −1/100
    • −100
    • 100
    • 1/100

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