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Multiplying Expressions with Indices
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Multiplying Expressions with Indices
Simplify each expression. When multiplying powers with the same base, add their indices. Show working where space is provided.
Foundation Skills
Multiply powers with the same base and simplify numerical coefficients.
1.Simplify: r³ × r⁵
2.Simplify: t⁶ × t²
3.Simplify: k × k⁷
4.Choose the simplified form of 4m² × 3m⁵.
- 7m⁷
- 12m⁷
- 12m¹⁰
- 12m³
5.Simplify: 6c³ × 2c⁴
6.Simplify: 7n² × 5n
Developing Skills
Multiply terms containing more than one variable, then expand brackets.
7.Simplify: 2uv³ × 5u⁴v²
8.Simplify: 3ab² × 4a³b⁵
9.Expand and simplify: 3x(2x² + 5x)
10.Expand and simplify: 2y²(4y³ − 3y)
11.Select every product that simplifies to 15a⁵b⁴.
- 3a²b × 5a³b³
- 5a⁴b × 3ab³
- 15a²b² × a³b²
- 5a³b⁴ × 3a²
Extension Challenges
Apply index laws to longer products and use them to solve problems.
12.Simplify: (3p²q)² × 2p⁴q³
13.Simplify: 2a³b × 5ab² × 3a²
14.A rectangle has area 10x⁴y³ square units and length 2xy. Find its width as an expression in simplest form.
15.Given q⁴ × qˣ = q¹¹, find x. State the index law used.
3 printable pages
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