Question

${(-\frac{5}{7})}^{-5}$ is equal to :

• A. ${\left(\frac{5}{7}\right)}^{-5}$
• B. ${\left(\frac{7}{5}\right)}^{-5}$
• C. ${(-\frac{7}{5})}^{-5}$
• D. ${(-\frac{7}{5})}^5$

Answer 1

The correct option is D

${(-\frac{7}{5})}^5$

We take the reciprocal of the fraction to change the sign of the exponent.

Hence,${(-\frac{5}{7})}^{-5}$ = $(-\frac{1}{\left(\frac{5}{7}\right)}{)}^5$

= ${(-\frac{7}{5})}^5$