Question

The value $\frac{{(-\frac{1}{2})}^5}{{(-\frac{1}{2})}^4}÷\frac{(-\frac{1}{8})}{(-\frac{1}{4})}$ is __________.

• A. $2$
• B. $0$
• C. $1$
• D. $-1$

Answer 1

Answer: (D)

$-1$

The given expression can be rewritten and solved as follows:

$\frac{\frac{{(-\frac{1}{2})}^5}{{(-\frac{1}{2})}^4}}{\frac{-\frac{1}{8}}{-\frac{1}{4}}}$

$=\frac{{(-\frac{1}{2})}^5}{{(-\frac{1}{2})}^4}\times \frac{-\frac{1}{4}}{-\frac{1}{8}}\{\because \frac{\frac{y}{x}}{\frac{a}{b}}=\frac{y}{x}\times \frac{b}{a}\}=\frac{-\frac{1}{32}}{\frac{1}{16}}\times \frac{-\frac{1}{4}}{-\frac{1}{8}}$

$=\frac{-\frac{1}{2}}{1}\times \frac{1}{\frac{1}{2}}$

$=\frac{-\frac{1}{2}}{\frac{1}{2}}$

$=-\frac{1}{2}\times \frac{2}{1}$

$=-1$

Hence, the value of the given division is $-1$.