Question

root x the power minus 2 by 3 root y the power 4 divided by root x y the power minus one by two​

Answer 1

this will be the answer of the question

Answer 2

The simplified form of given expression is $\dfrac{y^{9/4}}{x^{1/12}}$.

Step-by-step explanation:

Consider the given expression is

$\dfrac{(\sqrt{x})^{-2/3}(\sqrt{y})^4}{(\sqrt{xy})^{-1/2}}$

Using the properties of exponents we get

$\dfrac{(x^{1/2})^{-2/3}(y^{1/2})^4}{((xy)^{1/2})^{-1/2}}$                            $[\because \sqrt[n]{x}=x^{1/n}]$

$\dfrac{(x)^{-1/3}y^2}{(xy)^{-1/4}}$                           $[\because (a^m)^n=a^{mn}]$

$\dfrac{(x)^{-1/3}y^2}{(x)^{-1/4}(y)^{-1/4}}$             $[\because (ab)^n=a^nb^n]$

$(x)^{-1/3+1/4}y^{2+1/4}$               $[\because\dfrac{a^m}{a^n}=a^{m-n}]$

$(x)^{-1/12}y^{9/4}$

$\dfrac{y^{9/4}}{x^{1/12}}$

Therefore, the simplified form of given expression is $\dfrac{y^{9/4}}{x^{1/12}}$.

#Learn more

(49)^3/2-(49)^5/2/49

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