Apply all relevant properties of exponents to simplify the following expression. Assume all variables are nonzero. All exponents entered

Answer:
[tex]z^{10}[/tex]Explanation:
Given the expression below:
[tex]\mleft(\frac{z^9}{z^4}\mright)^2[/tex]Step 1: Apply the division law of indices.
If we have the same base, and the expression is being divided, subtract the indices.
[tex]\begin{gathered} =(z^{9-4})^2 \\ =(z^5)^2 \end{gathered}[/tex]Step 2: Multiply the indices by the index law of powers.
[tex]\begin{gathered} (a^m)^n=a^{m\times n} \\ \implies(z^5)^2=z^{5\times2}=z^{10} \end{gathered}[/tex]The simplified expression is z^(10).