The value of the product (32) × (32)
Question:

The value of the product (32) × (32)1/6 × (32)1/36 × _________ to ∞, is _________.

Solution:

$(32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times \ldots \ldots \ldots \infty$

$=(32)^{\left(1+\frac{1}{6}+\frac{1}{36}+\ldots \ldots\right)}$

Since $1+\frac{1}{6}+\frac{1}{6^{2}}+\ldots \ldots$ from an g. $\mathrm{p}$

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

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

$=\left(2^{5}\right)^{\frac{6}{5}}$

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

$=2^{6}=64$

i. e $(32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \ldots \ldots \ldots \infty$