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Exponents & radicals: FAQ

Frequently asked questions about exponents & radicals

What are exponent properties?

We can use these properties of exponents to help us simplify expressions involving exponents:
Product rule: xa×xb=xa+b. For example, x2×x3=x5.
Power rule: (xa)b=xab. For example, (x2)3=x6.
Quotient rule: xaxb=xab. For example, x5x2=x3.
Zero exponent rule: x0=1. For example, 70=1.

What are radicals?

A radical is a symbol that we use to write square roots, cube roots, and other roots. For example, 81 is the square root of 81, or the number we can multiply by itself to get 81. Another example is A83, which is the cube root of 8, or the number we can multiply by itself to get 8.
Practice with our Square roots exercise.
Practice with our Cube roots exercise.

What are some common ways to simplify square roots?

One common way to simplify square roots is to factor the radicand (the number inside the square root symbol) into perfect squares. For example, 50 can be simplified by factoring 50 into 25 times 2:

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