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6th grade · Math · Unit 12 of 17

Powers and Common Factors

Exponents and prime factorization

What your child practices

Reading and writing powers such as 3⁴, evaluating them, order of operations with powers, writing prime factorizations with exponents, and finding common factors and the greatest common factor.

Arizona Academic Standards learning standard: 6.EE.A.1 · writing and evaluating numerical expressions with whole-number exponents

How we explain it

Children can open this short lesson before they practice.

  1. An exponent tells how many times to multiply the base: 2³ = 2 × 2 × 2.
  2. A common factor divides two numbers evenly.
  3. To evaluate a power, multiply, then follow the order of operations.

Example: What is 2³ + 1? 2³ = 2 × 2 × 2 = 8. 8 + 1 = 9. Answer: 9

Powers and Common Factors in Arizona

In the Arizona Academic Standards, this is unit 12 of 17 in 6th grade Math, after Data & Graphs and before Dividing Fractions.

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

    Evaluate. Do the power first.

    2 + 4² = ?

    answer box

  2. Question 2

    Which shows the prime factorization of 28 using powers?

    • 2² × 7
    • 2² × 7²
    • 2 × 7²
    • 2³ × 7

  3. Question 3

    What is the value of 4²?

    answer box

  4. Question 4

    What is the greatest common factor of 15 and 9?

    answer box

  5. Question 5

    Which number is a common factor of 18 and 27?

    • 9
    • 10
    • 16

  6. Question 6

    What does 8⁴ mean?

    • 8 × 4
    • 8 × 8 × 8 × 8
    • 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
    • 8 + 4

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