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

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Question

(C) Given expression: $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$Step $1$: Simplify each term u

Vedclass · Accepted Answer

$214$

Vedclass · Answer

(C) Given expression: $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$Step $1$: Simplify each term using the property $a^{-n} = \frac{1}{a^n}$ or $\frac{1}{a^{-n}} = a^n$.Term $1$: $\frac{4}{(216)^{-\frac{2}{3}}} = 4 	imes (216)^{\frac{2}{3}} = 4 	imes ((6^3)^{\frac{2}{3}}) = 4 	imes 6^2 = 4 	imes 36 = 144$.Term $2$: $\frac{1}{(256)^{-\frac{3}{4}}} = 1 	imes (256)^{\frac{3}{4}} = (4^4)^{\frac{3}{4}} = 4^3 = 64$.Term $3$: $\frac{2}{(243)^{-\frac{1}{5}}} = 2 	imes (243)^{\frac{1}{5}} = 2 	imes ((3^5)^{\frac{1}{5}}) = 2 	imes 3^1 = 6$.Step $2$: Add the results together:$144 + 64 + 6 = 214$.Thus,the correct option is $C$.

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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