When you multiply powers of the same base, add the indices: x³ × x⁴ = x⁷, because that is seven x's multiplied together. When you divide, subtract the indices: y⁷ ÷ y⁴ = y³.
A power of a power multiplies the indices: (x⁵)² = x¹⁰. Two more facts follow from these rules. Any base to the power 0 is 1, and a negative index means one over: 3⁻² = 1/3² = 1/9. With numbers in front, work them out separately: 8x¹⁰ ÷ 4x⁶ = 2x⁴.
Worked example
Simplify (2x³)² × x
- (2x³)² = 2² × (x³)² = 4x⁶.
- 4x⁶ × x¹ = 4x⁷.
Answer:4x⁷
Key words
- index (power)
- the small raised number
- base
- the number or letter being raised to a power
- negative index
- means one over the power
Practise this
New questions every time.
Common Core-referenced: 8.EE.A.1