Special exponent laws

In addition to the actual exponent laws, there are a few more special cases.

1. Negative base

   if $x$ is straight: $(-a)^x=a^x$
   if $x$ is odd: $(-a)^x=-(a^x)$

2. Negative exponents

   $a^{-x}=\frac{1}{a^x}$

3. Fractions in exponents

   $a^{\frac{m}{n}}=\sqrt[n]{a^m}$

Examples

• $(-5)^2=5^2=25$
  $(-2)^3=-(2^3)=-8$


• $6^{-2}=\frac{1}{6^2}$ $=\frac{1}{36}$


• $2^\frac43=\sqrt[3]{2^4}$