Question

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

Answer 1

`z^(10)`

Explanation:

Given the expression below:

`\mleft((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* n) \\ \implies(z^5)^2=z^(5*2)=z^(10) \end{gathered}`

The simplified expression is z^(10).