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🔢 8th grade math · Counting & Numbers

Exponents, roots, big numbers

2³ × 2⁴ means 2 × 2 × 2 and then 2 × 2 × 2 × 2: seven 2s in all. So 2³ × 2⁴ = 2⁷. Same base, multiply: ADD the exponents. Same base, divide: SUBTRACT them.

Worked example

Find the missing exponent:
24 ÷ 23 = 2?
Answer: 1
Same base, so SUBTRACT the exponents: 4 − 3 = 1. 24 ÷ 23 = 21. Answer: 1.

For grown-ups: Integer exponents, square and cube roots, scientific notation. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 8.EE.A.1–4
What this practises, for teachers

Practices integer exponents, square and cube roots, scientific notation (8.EE.A.1–4). A printable sheet with its answer key, worked answers on the page, no accounts.

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For your class

🖨️ Printable sheet and key

On the board with this skill:

Try three

  1. Find the missing exponent:
    28 × 28 = 2?
    Show the answer and how
    Answer: 16
    Same base, so ADD the exponents: 8 + 8 = 16. 28 × 28 = 216. Answer: 16.
  2. Find the missing exponent:
    36 ÷ 32 = 3?
    Show the answer and how
    Answer: 4
    Same base, so SUBTRACT the exponents: 6 − 2 = 4. 36 ÷ 32 = 34. Answer: 4.
  3. Find the missing exponent:
    104 × 103 = 10?
    Show the answer and how
    Answer: 7
    Same base, so ADD the exponents: 4 + 3 = 7. 104 × 103 = 107. Answer: 7.

Before and after

Learn first: Negative number stories (7th)

Name: ____________________Date: ____________Score: ____ / 12

Exponents, roots, big numbers (8th grade)

  1. Find the missing exponent:
    107 ÷ 104 = 10?
  2. Find the missing exponent:
    57 ÷ 52 = 5?
  3. Find the missing exponent:
    36 ÷ 33 = 3?
  4. Find the missing exponent:
    32 × 38 = 3?
  5. Find the missing exponent:
    58 ÷ 57 = 5?
  6. Find the missing exponent:
    36 ÷ 32 = 3?
  7. Find the missing exponent:
    54 ÷ 52 = 5?
  8. Find the missing exponent:
    27 ÷ 26 = 2?
  9. Find the missing exponent:
    38 ÷ 36 = 3?
  10. Find the missing exponent:
    57 ÷ 52 = 5?
  11. Find the missing exponent:
    77 ÷ 75 = 7?
  12. Find the missing exponent:
    38 ÷ 36 = 3?

Answer key

  1. 3
  2. 5
  3. 3
  4. 10
  5. 1
  6. 4
  7. 2
  8. 1
  9. 2
  10. 5
  11. 2
  12. 2

More 8th grade skills: all 8th grade math skills, or every grade at math skills.