which expression is equivalent to $-32^{\frac{3}{5}}$?\n-8\n$-sqrt3{32^{5}}$\n$\frac{1}{sqrt3{32^{5}}}$\n$\fr…

Explanation:

Step1: Rewrite -32 as a power of 2

$-32=-2^5$

Step2: Substitute into the original expression

$(-32)^{\frac{3}{5}}=(-2^5)^{\frac{3}{5}}$

Step3: Apply power - of - a - power rule $(a^m)^n=a^{mn}$

$(-2^5)^{\frac{3}{5}}=(-1)^{\frac{3}{5}}\times(2^5)^{\frac{3}{5}}$. Since $(-1)^{\frac{3}{5}}=-1$ and $(2^5)^{\frac{3}{5}} = 2^{5\times\frac{3}{5}}=2^3$. $(-1)\times2^3=-8$

Answer:

A. -8