x^m y^m = ( y x )^ -m - Vidyadip

Question

$\frac{\text{x}^\text{m}}{\text{y}^\text{m}}=\Big(\frac{\text{y}}{\text{x}}\Big)^{-\text{m}}$

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Answer

$RHS =\Big(\frac{\text{y}}{\text{x}}\Big)^{-\text{m}}$
Using law of exponents, $\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{m}}=\frac{\text{a}^\text{m}}{\text{b}^\text{m}}$ and $\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}} [\because$ a is non-zero integers$]$
$\therefore \Big(\frac{\text{y}}{\text{x}}\Big)^{-\text{m}}=\frac{\text{y}^{-\text{m}}}{\text{y}^{-\text{m}}}$
$=\frac{\text{x}^\text{m}}{\text{y}^\text{m}} $
$LHS = RHS$

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