negative exponents

A negative exponent tells us to take the reciprocal of the base and make the exponent positive.

[latex]a^{-n}=\frac{1}{a^n}[/latex] where [latex]a\ne 0[/latex]

rational exponents

A rational exponent is another way of writing a root.

• The denominator of the exponent gives the root.

• The numerator of the exponent gives the power.

[latex]a^\frac{m}{n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m)[/latex]