Exponents & radicals: FAQ

We can use these properties of exponents help us to simplify expressions involving exponents:

Product rule: $x^a \times x^b = x^{a+b}$x, start superscript, a, end superscript, times, x, start superscript, b, end superscript, equals, x, start superscript, a, plus, b, end superscript. For example, $x^2 \times x^3 = x^5$x, squared, times, x, cubed, equals, x, start superscript, 5, end superscript.

Power rule: $(x^a)^b = x^{ab}$left parenthesis, x, start superscript, a, end superscript, right parenthesis, start superscript, b, end superscript, equals, x, start superscript, a, b, end superscript. For example, $(x^2)^3 = x^6$left parenthesis, x, squared, right parenthesis, cubed, equals, x, start superscript, 6, end superscript.

Quotient rule: $\dfrac{x^a}{x^b} = x^{a-b}$start fraction, x, start superscript, a, end superscript, divided by, x, start superscript, b, end superscript, end fraction, equals, x, start superscript, a, minus, b, end superscript. For example, $\dfrac{x^5}{x^2} = x^3$start fraction, x, start superscript, 5, end superscript, divided by, x, squared, end fraction, equals, x, cubed.

Zero exponent rule: $x^0 = 1$x, start superscript, 0, end superscript, equals, 1. For example, $7^0 = 1$7, start superscript, 0, end superscript, equals, 1.

Practice with our Multiply & divide powers (integer exponents) exercise.

Practice with our Powers of products & quotients (integer exponents) exercise.

A radical is a symbol that we use to write square roots, cube roots, and other roots. For example, $\sqrt{81}$square root of, 81, end square root is the square root of $81$81, or the number we can multiply by itself to get $81$81. Another example is $\sqrt[3]{8}$cube root of, 8, end cube root, which is the cube root of $8$8, or the number we can multiply by itself to get $8$8.

Practice with our Square roots exercise.

Practice with our Cube roots exercise.

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

Practice with our Simplify square roots exercise.