Simplified form of left[left(sqrt[5]{x^{-3 / | vedclass

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Question

(C) Given expression: $\left[\left(\sqrt[5]{x^{-3 / 5}}\right)^{-5 / 3}\right]^{5}$Using the property $\sqrt[n]{a} = a^{1/n}$,we can write $\sqrt[5]{x

Vedclass · Accepted Answer

$x$

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(C) Given expression: $\left[\left(\sqrt[5]{x^{-3 / 5}}ight)^{-5 / 3}ight]^{5}$Using the property $\sqrt[n]{a} = a^{1/n}$,we can write $\sqrt[5]{x^{-3/5}} = (x^{-3/5})^{1/5} = x^{-3/25}$.Now,applying the power rule $(a^m)^n = a^{m 	imes n}$ repeatedly:$= \left( (x^{-3/5})^{1/5} ight)^{-5/3 	imes 5}$$= (x^{-3/5})^{1/5 	imes -5/3 	imes 5}$$= (x^{-3/5})^{-25/15}$$= (x^{-3/5})^{-5/3}$$= x^{(-3/5) 	imes (-5/3)}$$= x^{1} = x$.

Simplified form of $\left[\left(\sqrt[5]{x^{-3 / 5}}\right)^{-5 / 3}\right]^{5}$ is

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