Question

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

Answer 1

Answer:

$z^{10}$

Explanation:

Given the expression below:

$\mleft(\frac{z^9}{z^4}\mright)^2$

Step 1: Apply the division law of indices.

If we have the same base, and the expression is being divided, subtract the indices.

$\begin{gathered} =(z^{9-4})^2 \\ =(z^5)^2 \end{gathered}$

Step 2: Multiply the indices by the index law of powers.

$\begin{gathered} (a^m)^n=a^{m\times n} \\ \implies(z^5)^2=z^{5\times2}=z^{10} \end{gathered}$

The simplified expression is z^(10).