Find the value of $\frac{x}{y}$ if $(\frac{3}{5})^{4}$ $\times$ $(\frac{15}{10})^{4}$=$(\frac{x}{y})^{4}$
Solution:
$(\frac{3}{5})^{4}$ $\times$ $(\frac{15}{10})^{4}$=$(\frac{x}{y})^{4}$
$a^4\times b^4 = (ab)^4$
$(\frac{3}{5})^{4}$ $\times$ $(\frac{15}{10})^{4}$ = $(\frac{3}{5} \times \frac{15}{10})^4 $
$(\frac{3}{5})^{4}$ $\times$ $(\frac{15}{10})^{4}$ = $(\frac{9}{10})^4$ [$5 \times 3 = 15 ; 3 \times 3 = 9$]
$(\frac{9}{10})^4$ = $(\frac{x}{y})^{4}$
Powers are equal , so we can cancel them,
$\frac{9}{10} = \frac{x}{ y}$
$\frac{x}{ y} = \frac{9}{10}$
Therefore the value of $\frac{x}{y} = \frac{9}{10}$
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