Exponents & Radicals
Use the exponent rules and write radicals as fractional powers.
The rules
- Same base: multiply means add exponents, divide means subtract, a power of a power means multiply.
- a⁰ = 1 and a⁻ⁿ = 1/aⁿ.
- √x = x^(1/2), and the nth root is x^(1/n).
- Simplify radicals by pulling out perfect squares: √72 = 6√2.
Watch out: Adding exponents when you should multiply them in (x²)³ = x⁶.
Worked example
Simplify √72.
- 72 = 36 · 2.
- √36 = 6, so √72 = 6√2.
Answer: 6√2
Try it yourself
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