Question

${\left(64\right)}^{-\frac{1}{2}}-{\left(-32\right)}^{-\frac{4}{5}}=?$

• A. 3/8
• B. 1/16
• C. 3/16
• D. None of these

Answer 1

The correct option is B

1/16

$\begin{array}{c}{\left(64\right)}^{-\frac{1}{2}}-{\left(-32\right)}^{-\frac{4}{5}}={\left(8^2\right)}^{-\frac{1}{2}}-{\left\{\left(-2^5\right)\right\}}^{-\frac{4}{5}}=8^{2\times \frac{\left(-1\right)}{2}}-2{\left(-2\right)}^{5\times \frac{\left(-4\right)}{5}}=8^{-1}-{\left(-2\right)}^{-4}\\ =\frac{1}{8}-\frac{1}{{\left(-2\right)}^4}=\left(\frac{1}{8}-\frac{1}{16}\right)=\frac{1}{16}.\end{array}$