Question

${\left(\frac{3}{4}\right)}^5÷{\left(\frac{3}{5}\right)}^5$ is equal to

• A. ${\left(\frac{5}{4}\right)}^5$
• B. ${\left(\frac{5}{3}\right)}^5$
• C. ${\left(\frac{1}{4}\right)}^5$
• D. ${\left(\frac{1}{5}\right)}^5$

Answer 1

The correct option is A

${\left(\frac{5}{4}\right)}^5$

$Given,{\left(\frac{3}{4}\right)}^5÷{\left(\frac{3}{5}\right)}^5$

=$\frac{(\frac{3}{4}{)}^5}{(\frac{3}{5}{)}^5}$

$\because \frac{a^m}{b^m}=(\frac{a}{b}{)}^m$

=$(\frac{\left(\frac{3}{4}\right)}{\left(\frac{3}{5}\right)}{)}^5$

=${(\frac{3}{4}\times \frac{5}{3})}^5$

=${\left(\frac{5}{4}\right)}^5$