Question

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

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

Answer 1

The correct option is B

$-3$

Let's simplify ${64}^{-\frac{1}{3}}\left[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}\right]$

$={64}^{-\frac{1}{3}}\times {64}^{\frac{1}{3}}-{64}^{-\frac{1}{3}}\times {64}^{\frac{2}{3}}$

$={64}^{-\frac{1}{3}+\frac{1}{3}}-{64}^{\frac{-1}{3}+\frac{2}{3}}$ [$a^x\times a^y=a^{x+y}$ is used]

$={64}^{\frac{-1+1}{3}}-{64}^{\frac{-1+2}{3}}$

$={64}^0-{64}^{\frac{1}{3}}=1-\sqrt[3]{64}$ [$$\begin{gathered} a^0=1 \\ {a}^{\frac{1}{x}}=\sqrt[x]{a} \end{gathered}$$ is used]

$$\begin{gathered} =1-4 \\ =-3 \end{gathered}$$

Hence, ${64}^{-\frac{1}{3}}\left[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}\right]=-3$

Hence, option B is correct.