Indices and surds
Lesson 9 of 14
Index laws
Objective. Multiply, divide and raise powers with the same base.
The key idea
Multiplying adds indices, dividing subtracts them, and a power of a power multiplies them: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ.
Worked example
Simplify (x³)⁴ ÷ x⁵.
- 1(x³)⁴ = x¹².
- 2x¹² ÷ x⁵ = x⁷.
Answer: x⁷
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Adding indices when powers are raised to powers.
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