Exponential functions > Exponents and powers
12345Exponents and powers

## Theory

The following properties of powers and exponents are true for any positive base $g$ and any real numbers $a$ and $b$:

• ${g}^{0}=1$

• ${g}^{-a}=\frac{1}{{g}^{a}}$

• ${g}^{\frac{1}{a}}=\sqrt[a]{g}$ as long as $a>0$.

• ${g}^{a+b}={g}^{a}\cdot {g}^{b}$

• ${g}^{a-b}=\frac{{g}^{a}}{{g}^{b}}$

• ${\left({g}^{a}\right)}^{b}={g}^{a}\cdot b$