Question

Find the value of ${125}^{-\frac{2}{3}}({125}^{\frac{4}{3}}-{125}^{\frac{2}{3}})$.

• A. $25$
• B. $625$
• C. $24$
• D. $600$

Answer 1

The correct option is C $24$

We know that the cube of $5$ is $125$, i.e., $5^3=125$.

Substitute $5^3$ for $125$ in the given equation to simplify.

$\begin{array}{cc}{125}^{-\frac{2}{3}}({125}^{\frac{4}{3}}-{125}^{\frac{2}{3}})& =(5^3{)}^{-\frac{2}{3}}\left(\right(5^3{)}^{\frac{4}{3}}-\left(5^3{)}^{\frac{2}{3}}\right)\\ & =5^{3\times (-\frac{2}{3})}(5^{3\times \frac{4}{3}}-5^{3\times \frac{2}{3}})\\ & =5^{-2}(5^4-5^2)\\ & ={25}^{-1}(625-25)\\ & =\frac{1}{25}\left(600\right)\\ & =24\end{array}$