Question

Evaluate.     −64125‾‾‾‾‾√3

Answer 1

The given expression is :$\sqrt[3]{\frac{-64}{125}}$

64 can be written as 4x4x4=$4^{3}$

125 =5x5x5=$5^{3}$

The given expression can be written as :

$\sqrt[3]{\frac{-64}{125}} =\sqrt[3]{\frac{(-4)^{3}}{5^{3}}} =[( \frac{-4}{5})^{3} }]^\frac{1}{3}$

Applying power rule of indices :

Powers are multiplied .

$\frac{1}{3} times 3 = 1.$

= $\frac{-4}{5}$

The first option $\frac{-4}{5}$ is the right asnwer

Answer 2

-4/5 is correct, since (-4/5)³ = -4*-4*-4/(5*5*5) = -64/125