Mathematics: Simplify and write in radical form: ((x^3 * y^-2) / xy)^-(1/5)

How can I answer this? Everything is so spaced out sorry!...

Simplify and write in radical form: ((x^3 * y^-2)

memeE15

12.01.2022

$\sqrt[5]{(\frac{y^3}{x^2})}$

Step-by-step explanation:

$(\frac{x^3\times y^{-2}}{xy})^{\frac{-1}{5}}$

Now we will use the quotient rule of exponent which is given by

$\frac{x^a}{x^b}=a^{a-b}$

Using this property, we get

$({x^{3-1}\times y^{-2-1}})^{\frac{-1}{5}}$

On simplifying, we get

$({x^{2}\times y^{-3}})^{\frac{-1}{5}}$

Now, use the property, $x^{-a}=\frac{1}{x^a}$

$(\frac{x^2}{y^3})^{\frac{-1}{5}}$

Now, we can use the rule $x^{1/a}=\sqrt[a]{x}$

$(\frac{y^3}{x^2})^{\frac{1}{5}}\\\\=\sqrt[5]{(\frac{y^3}{x^2})}$

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