First, let's simplify the left part of the equation using the following properties:
[tex]\begin{gathered} \frac{a^b}{a^c}=a^{b-c} \\ (a^b)^c=a^{b\cdot c} \end{gathered}[/tex]
So we have:
[tex](\frac{13^0^{}}{13^3})^{\frac{1}{3}}=(13^{0-3})^{\frac{1}{3}}=(13^{-3})^{\frac{1}{3}}=13^{-3\cdot\frac{1}{3}}=13^{-1}[/tex]
The statement is wrong because the exponent of the numerator is 0 and not 1, like the exponent on the second given equation (which is correct), so the result is different.
