Question

(-32)^9/5

Please show work and if it's not a real number, please write it and explain why it isn't a real number. Thank you in advance.

Answer 1

$\textbf{Ans.:}$

$\text{Let}\quad x = (-32)^{\dfrac{9}{5}}$

$\Rightarrow x =\left(\left(-32 \right ) ^{\dfrac{1}{5}} \right )^9$

$\Rightarrow x =\left(\left((-2)^5 \right ) ^{\dfrac{1}{5}} \right )^9$

$\Rightarrow x =\left(\left(-2 \right )^9=-512$