# Exponents, Radicals and Logarithms

**In this video**

@02:30 = the correct term is commutative.

Exponents

- $(a^m)^n = a^{mn}$
- $a^m \cdot a^n = a^{m + n}$
- $\dfrac{a^m}{a^n} = a^{m - n}$
- $(ab)^m = a^m \cdot b^m$

Radicals

- $a^{1/n} = \sqrt[n]{a}$
- $a^{m/n} = \sqrt[n]{a^m}$

Logarithms

- For $y = b^x$, then $x = \log_b y$
- $\log_b x^m = m \log_b x$
- $\log_b (xy) = \log_b x + \log_b y$
- $\log_b \left( \dfrac{x}{y} \right) = \log_b x - \log_b y$
- $\log_b b = 1$
- $\log_b 1 = 0$
- $\log_e x = \ln x$
- $\log_{10} x = \log x$