[(3^{2})^{6}]^{5} = 9^{?} | vedclass

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Question

(A) Given the expression: $[(3^{2})^{6}]^{5} = 9^{x}$.Using the power of a power rule $(a^{m})^{n} = a^{m 	imes n}$,we simplify the left side:$(3^{2

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) Given the expression: $[(3^{2})^{6}]^{5} = 9^{x}$.Using the power of a power rule $(a^{m})^{n} = a^{m 	imes n}$,we simplify the left side:$(3^{2 	imes 6})^{5} = (3^{12})^{5} = 3^{12 	imes 5} = 3^{60}$.Now,express the right side with base $3$:$9^{x} = (3^{2})^{x} = 3^{2x}$.Equating both sides:$3^{60} = 3^{2x}$.Since the bases are equal,the exponents must be equal:$60 = 2x$.Solving for $x$:$x = 30$.

$[(3^{2})^{6}]^{5} = 9^{?}$

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