Index laws

• Powers multiplied together should be summed

  $a^na^m=$ $a^{n+m}$
• A power to the power of another power should be multiplied

  $\left(a^n\right)^m=$ $a^{nm}$
• For negative powers you apply the power normally and take the reciprocal

  $a^{-n}=$ $\frac{1}{a^n}$
• If the power is 1 over n then you take the nth root

  $a^{\frac{1}{n}}=$ $\sqrt[n]{a}$
• Anything to the power 0 is 1

  $a^0=$ $1$