Answer: First option.
Step-by-step explanation:
We need to remember that:
[tex]\sqrt[n]{a^n}=a[/tex]
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]
And, according to the Power of a power property we know that:
[tex](a^m)^n=a^{(mn)}[/tex]
Knowing this, we can descompose 32 into its prime factors:
[tex]32=2*2*2*2*2=2^5[/tex]
Then we can rewrite the expression as:
[tex]=\sqrt[5]{(-32)^3}\\\\=\sqrt[5]{(-2^5)^3}[/tex]
Finally, simplifying the expression, we get:
[tex]=\sqrt[5]{(-2)^{15}}\\\\=(-2)^3\\\\=-8[/tex]
This matches with the first option.
