Question

Help me solve these. I’d like to know how to solve and know which answer choice is correct or not too. I can rewrite this if you are having a hard time reading the photo

Answer 1

Given the following expression:

`(\sqrt[3]{8})^5`

We will simplify the expression to find the equivalent expressions:

We will use the following rules of the exponents:

`\begin{gathered} (a^m)^n=a^(mn) \\ \\ \sqrt[m]{a^n}=a^{(n)/(m)} \end{gathered}`

So, the given expression can be written as follows:

`\begin{gathered} (\sqrt[3]{8})^5=(8^{(1)/(3)})^5=8^{(5)/(3)} \\ \\ =(2^3)^{(5)/(3)}=2^5 \\ \\ =32 \end{gathered}`

So, there are 3 correct equivalent expressions.

So, the answer will be:

`\begin{gathered} 32 \\ 2^5 \\ 8^{(5)/(3)} \end{gathered}`