Question

Simplify:${64}^{-\frac{1}{3}}[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}]$

• A. $\frac{1}{3}$
• B. $-3$
• C. $\frac{2}{3}$
• D. $(3{)}^{-2}$

Answer 1

The correct option is B

$-3$

${64}^{-\frac{1}{3}}[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}]=\left(4^3{)}^{-\frac{1}{3}}\right[(4^3{)}^{\frac{1}{3}}-(4^3{)}^{\frac{2}{3}}]=4^{3\times (-\frac{1}{3})}(4^{3\times \frac{1}{3}}-4^{3\times \frac{2}{3}})=4^{-1}(4-4^2)=\frac{1}{4}(4-16)=\frac{1}{4}\times (-12)=-3$