Find the value of sqrt[5]{(243)^{-3}}. | vedclass

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Question

(A) Given expression is $\sqrt[5]{(243)^{-3}}$.We know that $243 = 3^5$.Substituting this into the expression: $\sqrt[5]{(3^5)^{-3}}$.Using the power

Vedclass · Accepted Answer

$1/27$

Vedclass · Answer

(A) Given expression is $\sqrt[5]{(243)^{-3}}$.We know that $243 = 3^5$.Substituting this into the expression: $\sqrt[5]{(3^5)^{-3}}$.Using the power rule $(a^m)^n = a^{m 	imes n}$,we get $(3^5)^{-3} = 3^{-15}$.Now,the expression becomes $\sqrt[5]{3^{-15}}$.Using the radical rule $\sqrt[n]{x} = x^{1/n}$,we get $(3^{-15})^{1/5} = 3^{-15 	imes 1/5} = 3^{-3}$.$3^{-3} = \frac{1}{3^3} = \frac{1}{27}$.

Find the value of $\sqrt[5]{(243)^{-3}}$.

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