The given expression is :[tex] \sqrt[3]{\frac{-64}{125}} [/tex]
64 can be written as 4x4x4=[tex] 4^{3} [/tex]
125 =5x5x5=[tex] 5^{3} [/tex]
The given expression can be written as :
[tex] \sqrt[3]{\frac{-64}{125}} =\sqrt[3]{\frac{(-4)^{3}}{5^{3}}} =[( \frac{-4}{5})^{3} }]^\frac{1}{3} [/tex]
Applying power rule of indices :
Powers are multiplied .
[tex] \frac{1}{3} times 3 = 1. [/tex]
= [tex] \frac{-4}{5} [/tex]
The first option [tex] \frac{-4}{5} [/tex] is the right asnwer
