Question

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

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

Answer 1

The correct option is D

${\left(\frac{7}{5}\right)}^5$

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

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

= ${\left(\frac{7}{5}\right)}^5$