Find the simplified value of 63 sqrt{(729)^{- | vedclass

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Question

(D) Given expression: $63 \sqrt{(729)^{-\frac{2}{3}}+(343)^{-\frac{2}{3}}}$Using the property $a^{-n} = \frac{1}{a^n}$,we rewrite the expression as:$6

Vedclass · Accepted Answer

$\sqrt{130}$

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(D) Given expression: $63 \sqrt{(729)^{-\frac{2}{3}}+(343)^{-\frac{2}{3}}}$Using the property $a^{-n} = \frac{1}{a^n}$,we rewrite the expression as:$63 \sqrt{\frac{1}{(729)^{\frac{2}{3}}} + \frac{1}{(343)^{\frac{2}{3}}}}$Calculate the powers:$(729)^{\frac{2}{3}} = (9^3)^{\frac{2}{3}} = 9^2 = 81$$(343)^{\frac{2}{3}} = (7^3)^{\frac{2}{3}} = 7^2 = 49$Substitute these values back into the expression:$63 \sqrt{\frac{1}{81} + \frac{1}{49}} = 63 \sqrt{\frac{49 + 81}{81 \cdot 49}}$Simplify the square root:$63 \cdot \frac{\sqrt{49 + 81}}{\sqrt{81} \cdot \sqrt{49}} = 63 \cdot \frac{\sqrt{130}}{9 \cdot 7}$Since $9 \cdot 7 = 63$,the expression becomes:$63 \cdot \frac{\sqrt{130}}{63} = \sqrt{130}$

Find the simplified value of $63 \sqrt{(729)^{-\frac{2}{3}}+(343)^{-\frac{2}{3}}} ?$

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