Multiply, divide and raise powers of the same number, the zero index, and the same laws with letters.
What you will learn
- Multiply and divide powers of the same base
- Raise a power to a power
- Use a⁰ = 1
- Simplify terms like 3x⁴ × 4x⁵ and (2x³)⁴
Three laws
For powers of the same number:
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
Why: 5³ × 5² = (5 × 5 × 5) × (5 × 5) = 5⁵. Counting the fives is adding the indices.
And a⁰ = 1, because 5³ ÷ 5³ = 5⁰ and anything divided by itself is 1. This is true for any number that is not zero, negative ones too: (−4)⁰ = 1, and x⁰ = 1.
The laws work in a chain: (3⁶ × 3⁴) ÷ 3⁷ = 3¹⁰ ÷ 3⁷ = 3³.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Three laws
- With letters and numbers in front
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Same
In this unit: Powers, roots and standard form
Squares, cubes and roots, the laws of indices (negative and fractional too), and very large and very small numbers in standard form.