Find the value of frac{4}{(216)^{-frac{2}{3}} | vedclass

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Question

(A) Given expression: $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$Using the property $a^{-n} = \

Vedclass · Accepted Answer

$214$

Vedclass · Answer

(A) Given expression: $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$Using the property $a^{-n} = \frac{1}{a^n}$,we can rewrite the expression as:$4(216)^{\frac{2}{3}} + (256)^{\frac{3}{4}} + 2(243)^{\frac{1}{5}}$Expressing the bases as powers:$216 = 6^3$,$256 = 4^4$,$243 = 3^5$Substituting these values:$= 4(6^3)^{\frac{2}{3}} + (4^4)^{\frac{3}{4}} + 2(3^5)^{\frac{1}{5}}$Using the power rule $(a^m)^n = a^{m 	imes n}$:$= 4(6^{3 	imes \frac{2}{3}}) + (4^{4 	imes \frac{3}{4}}) + 2(3^{5 	imes \frac{1}{5}})$$= 4(6^2) + 4^3 + 2(3^1)$Calculating the values:$= 4(36) + 64 + 2(3)$$= 144 + 64 + 6$$= 214$

Find the value of $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$

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