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Index Laws Practice
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Index Laws Practice
Simplify each expression using index laws. Assume variables are non-zero where division is involved. Show working for written questions.
Understanding Indices
1.Which expression shows 6⁴ as repeated multiplication?
- 6 × 4
- 6 + 6 + 6 + 6
- 6 × 6 × 6 × 6
- 4 × 4 × 4 × 4 × 4 × 4
2.Simplify 3⁵ × 3².
- 3¹⁰
- 3⁷
- 9⁷
- 3³
3.Simplify 8⁹ ÷ 8⁴.
- 8¹³
- 8⁵
- 2⁵
- 8²
4.Select every expression equivalent to 4⁶.
- 4² × 4⁴
- 4⁹ ÷ 4³
- 4 × 4 × 4 × 4 × 4 × 4
- 4⁸ ÷ 4³
Apply the Index Laws
5.Complete the exponent: 5³ × 5⁴ = 5^□.
6.Complete the exponent: 7¹⁰ ÷ 7⁶ = 7^□.
7.Find the missing exponent: 2² × 2^□ = 2⁹.
8.Find the missing exponent: 10⁸ ÷ 10^□ = 10³.
9.Simplify 9³ × 9⁵. Show the index law you use.
10.Simplify 12⁷ ÷ 12². Show the index law you use.
11.A cube has side length 4 cm. Write its volume as a power, then calculate the volume in cubic centimetres.
12.In one sentence, describe what happens to the exponents when you multiply powers that have the same base.
Challenge Questions
13.If 3ˣ × 3⁴ = 3¹¹, find x.
14.Simplify (2⁶ × 2³) ÷ 2⁵, leaving your answer as a power of 2.
15.Use the pattern in 6⁴ ÷ 6⁴ = 1 to predict the value of 6⁰. Explain briefly.
16.Simplify (5²)³, giving your answer as a single power of 5.
3 printable pages
Page 1
Page 2
Page 3
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