The product (32)(32)^{1/6}(32)^{1/36} dots in | vedclass

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Question

(C) Let the given expression be $P = (32)(32)^{1/6}(32)^{1/36} \dots \infty$.Since the bases are the same, we can add the exponents: $P = (32)^{1 + 1/

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(C) Let the given expression be $P = (32)(32)^{1/6}(32)^{1/36} \dots \infty$.Since the bases are the same, we can add the exponents: $P = (32)^{1 + 1/6 + 1/36 + \dots \infty}$.The exponent is an infinite geometric series with the first term $a = 1$ and common ratio $r = 1/6$.The sum of an infinite geometric series is given by $S = a / (1 - r)$.Substituting the values, $S = 1 / (1 - 1/6) = 1 / (5/6) = 6/5$.Therefore, $P = (32)^{6/5}$.Since $32 = 2^5$, we have $P = (2^5)^{6/5} = 2^{(5 	imes 6/5)} = 2^6$.$2^6 = 64$.

The product $(32)(32)^{1/6}(32)^{1/36} \dots \infty$ is

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