The product (32),(32)^ 1 6 (32)^ 1 36 to is equal to: - Vidyadip

MCQ

The product $(32),(32)^{\frac{1}{6}}(32)^{\frac{1}{36}}\ \dots\text{ to }\infty$ is equal to:

✓
$64$
B
$16$
C
$32$
D
$0$

✓

Answer

Correct option: A.

$64$

$32\times32^{\frac{1}{6}}\times32^{\frac{1}{36}}\times\ \cdots\infty$
$=32^{\big(1+\frac{1}{6}+\frac{1}{36}+\ \cdots\infty\big)}$
$=32^{\Bigg(\frac{1}{1-\frac{1}{6}}\Bigg)}$
$[\because$ it is a $G.P. ]$
$=32^{\big(\frac65\big)}$
$=\big(2^5\big)^{\big(\frac65\big)}$
$=2^6$
$=64$

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