Exponents and radicals
Exponent rules, negative and fraction exponents, and simplifying square roots.
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About Exponents and radicals
Exponents are a short way to write repeated multiplication: 2³ = 2 × 2 × 2 = 8. A handful of rules let you simplify almost any expression with powers in it, and the same rules explain what negative and fraction exponents mean.
Radicals are the other side of exponents. A square root undoes a square, and simplifying one means pulling out every perfect square factor, like √50 = √25 × √2 = 5√2.
Keep in mind
- Multiply: add the exponents. x² × x³ = x⁵.
- Divide: subtract the exponents. x⁵ ÷ x² = x³.
- Power of a power: multiply the exponents. (x²)³ = x⁶.
- Anything (except 0) to the power 0 is 1.
- A negative exponent means one over: x⁻² = 1/x².
- A fraction exponent is a root: x to the power 1/2 is √x.
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