Question
Solve for $x:\sqrt{\left(\frac{3}{5}\right)^{x+3}}=\frac{27^{-1}}{125^{-1}}$
✓
Answer
$\sqrt{\left(\frac{3}{5}\right)^{x+3}}=\frac{27^{-1}}{125^{-1}}$
$\Rightarrow\left(\frac{3}{5}\right)^{(x+3) \times\left(\frac{1}{2}\right)}=\frac{\left(3^3\right)^{-1}}{\left(5^3\right)-1}$
$\Rightarrow\left(\frac{3}{5}\right)^{\frac{x+3}{2}}=\left(\frac{3}{5}\right)^{-3}$
$\Rightarrow \frac{x+3}{2}=-3$
$\Rightarrow x+3=-6$
$\Rightarrow x=-9 .$
$\Rightarrow\left(\frac{3}{5}\right)^{(x+3) \times\left(\frac{1}{2}\right)}=\frac{\left(3^3\right)^{-1}}{\left(5^3\right)-1}$
$\Rightarrow\left(\frac{3}{5}\right)^{\frac{x+3}{2}}=\left(\frac{3}{5}\right)^{-3}$
$\Rightarrow \frac{x+3}{2}=-3$
$\Rightarrow x+3=-6$
$\Rightarrow x=-9 .$
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