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

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Solution

$(32) (32)^{\frac{1}{6}} (32)^{\frac{1}{36}} \dots . \dots . . . . . . \infty$

$= (32)^{1 + \frac{1}{6} + \frac{1}{36} + \dots . \infty}$

$= (32)^{\frac{1}{1 - \frac{1}{6}}}$

$= (32)^{\frac{6}{5}}$

$= 2^{5 \frac{6}{5}}$

$= 2^{6} = 64$

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The product (32)(32)1/6(32)1/36. to ∞ is?

(32)(32)16(32)136….…......∞=(32)1+16+136+….∞=(32)11−16=(32)65=2565=26=64

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

$(32) (32)^{\frac{1}{6}} (32)^{\frac{1}{36}} \dots . \dots . . . . . . \infty$

$= (32)^{1 + \frac{1}{6} + \frac{1}{36} + \dots . \infty}$

$= (32)^{\frac{1}{1 - \frac{1}{6}}}$

$= (32)^{\frac{6}{5}}$

$= 2^{5 \frac{6}{5}}$

$= 2^{6} = 64$