The index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ and (aᵐ)ⁿ = aᵐⁿ. Also a⁰ = 1 and a⁻ⁿ = 1/aⁿ. Deal with the numbers and the letters separately.
(4m²)³ = 4³ × m⁶ = 64m⁶, because the power applies to everything inside the bracket. 6x³ ÷ (2x⁷) = 3x⁻⁴, which can also be written 3/x⁴. With several letters, apply the laws to each letter on its own.
Worked example
Simplify (3x²y)³
- Cube the number: 3³ = 27.
- Multiply each index by 3: x⁶ and y³.
Answer:27x⁶y³
Key words
- index laws
- rules for multiplying and dividing powers
- zero index
- anything to the power 0 is 1
- negative index
- one over the positive power
Practise this
New questions every time.
Common Core-referenced: HSN-RN.A.2