Which of the following is not equal to left[l | vedclass

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Question

(A) Given expression is $\left[\left(\frac{5}{6}ight)^{\frac{1}{5}}ight]^{-\frac{1}{6}}$.Using the power rule $(a^m)^n = a^{m 	imes n}$,we get:$\

Vedclass · Accepted Answer

$\left(\frac{5}{6}\right)^{\frac{1}{5}-\frac{1}{6}}$

Vedclass · Answer

(A) Given expression is $\left[\left(\frac{5}{6}ight)^{\frac{1}{5}}ight]^{-\frac{1}{6}}$.Using the power rule $(a^m)^n = a^{m 	imes n}$,we get:$\left(\frac{5}{6}ight)^{\frac{1}{5} 	imes (-\frac{1}{6})} = \left(\frac{5}{6}ight)^{-\frac{1}{30}}$.Now,let's evaluate the options:$A$: $\left(\frac{5}{6}ight)^{\frac{1}{5}-\frac{1}{6}} = \left(\frac{5}{6}ight)^{\frac{6-5}{30}} = \left(\frac{5}{6}ight)^{\frac{1}{30}}$. This is not equal to $\left(\frac{5}{6}ight)^{-\frac{1}{30}}$.$B$: $\frac{1}{\left[\left(\frac{5}{6}ight)^{\frac{1}{5}}ight]^{\frac{1}{6}}} = \frac{1}{\left(\frac{5}{6}ight)^{\frac{1}{30}}} = \left(\frac{5}{6}ight)^{-\frac{1}{30}}$. This is equal.$C$: $\left(\frac{6}{5}ight)^{\frac{1}{30}} = \left(\left(\frac{5}{6}ight)^{-1}ight)^{\frac{1}{30}} = \left(\frac{5}{6}ight)^{-\frac{1}{30}}$. This is equal.$D$: $\left(\frac{5}{6}ight)^{-\frac{1}{30}}$. This is equal.Therefore,option $A$ is not equal to the given expression.

Which of the following is not equal to $\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{-\frac{1}{6}}?$

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