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Question

# Simplify the expression.$\left(\frac{x^{2}}{y^{3}}\right)^{-5}$

Solution

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$\text{\color{#4257b2}Recall that: \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}}$

$\left(\dfrac{x^2}{y^3}\right)^{-5} =\left(\dfrac{y^3}{x^2}\right)^{5}$

$\text{\color{#4257b2}Recall that: \left(\dfrac{a}{b}\right)^{n}=\dfrac{a^n}{b^n}}$

$=\dfrac{(y^3)^5}{(x^2)^5}$

$\text{\color{#4257b2}Recall that: (a^m)^n=a^{m\cdot n}}$

$=\dfrac{y^{3\cdot5}}{x^{2\cdot5}}$

$=\dfrac{y^{15}}{x^{10}}$

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