Given the following expression:
[tex](\sqrt[3]{8})^5[/tex]
We will simplify the expression to find the equivalent expressions:
We will use the following rules of the exponents:
[tex]\begin{gathered} (a^m)^n=a^{mn} \\ \\ \sqrt[m]{a^n}=a^{\frac{n}{m}} \end{gathered}[/tex]
So, the given expression can be written as follows:
[tex]\begin{gathered} (\sqrt[3]{8})^5=(8^{\frac{1}{3}})^5=8^{\frac{5}{3}} \\ \\ =(2^3)^{\frac{5}{3}}=2^5 \\ \\ =32 \end{gathered}[/tex]
So, there are 3 correct equivalent expressions.
So, the answer will be:
[tex]\begin{gathered} 32 \\ 2^5 \\ 8^{\frac{5}{3}} \end{gathered}[/tex]
