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Index Laws Practice
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Index Laws Practice
Simplify each expression using index laws. Assume all variables are non-zero where needed. Give answers with positive indices unless a question asks otherwise.
Choose and Match
Select the best answer for each multiple-choice question. Then match each law name to its formula.
1.Simplify p⁶ × p⁻².
- p⁴
- p⁸
- p⁻⁴
- 1
2.Simplify t⁵⁄³ ÷ t²⁄³.
- t
- t⁷⁄³
- t¹⁰⁄⁹
- t⁻¹
3.Expand and simplify (−3r²s⁻¹)².
- 9r⁴s⁻²
- −6r⁴s⁻²
- 9r⁴s²
- −9r²s⁻²
4.Evaluate 4⁰ + 2⁻³.
- 9⁄8
- 1⁄8
- 8
- 1⁄9
5.Match each index law name with the formula that describes it. Use each formula once.
- Product of powers
- Quotient of powers
- Zero index
- Power of a power
- Power of a product
- Power of a quotient
- (a ÷ b)ᵐ = aᵐ ÷ bᵐ
- (aᵐ)ⁿ = aᵐⁿ
- (ab)ᵐ = aᵐbᵐ
- aᵐ × aⁿ = aᵐ⁺ⁿ
- a⁰ = 1, for a ≠ 0
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Simplify and Explain
Show enough working to make your use of the index laws clear.
6.Simplify (d⁻³)⁴.
7.Simplify k⁷⁄⁴ ÷ k³⁄⁴.
8.Simplify fully and write with positive indices: (2u¹⁄² ÷ v⁻³)³.
9.In one sentence, explain why q⁰ = 1 when q ≠ 0.
10.Simplify fully and write with positive indices: (z⁵⁄²w⁻³) ÷ (z¹⁄²w²).
11.Simplify fully and write with positive indices: (5a⁻²b³) ÷ (10a²b⁻¹).
12.Simplify fully and write with positive indices: (x⁻¹y²)² × (x³ ÷ y).
13.Simplify and evaluate: 16¹⁄² × 8⁻¹⁄³.
14.Challenge: Simplify fully and write with positive indices: (m⁴⁄³n⁻²)² ÷ (m¹⁄³n⁻¹).
3 printable pages
Page 1
Page 2
Page 3
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