#math/calculus For integers $m,n$ and a nonzero base $a$ when a negative exponent occurs, $ a^{m}a^{n}=a^{m+n},\qquad \frac{a^{m}}{a^{n}}=a^{m-n},\qquad (a^{m})^{n}=a^{mn},\qquad a^{-n}=\frac{1}{a^{n}}. $ Also, $(ab)^{n}=a^{n}b^{n}$ and $(a/b)^{n}=a^{n}/b^{n}$ when $b\neq 0$. For a rational exponent $r=m/n$ in lowest terms, $ a^{m/n}=\sqrt[n]{a^{m}}=\left(\sqrt[n]{a}\right)^{m}, $ whenever the real-valued expression is defined. If $n$ is even, this requires $a\geq 0$; if the exponent is negative, it also requires $a\neq 0$. > [!Warning] > Exponent rules do not override domain restrictions. In particular, $0^{0}$ is undefined, and an even root of a negative real number is not real.