Question

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

• A. 16
• B. 32
• C. 64
• D. 0
• E. 62

Answer 1

Answer: (C)

$(32){(32)}^{1/6}{(32)}^{(1/36)}....$
$={32}^{1+\frac{1}{6}+\frac{1}{36}+.....}$
$={32}^{\frac{1}{1-1/6}}={(32)}^{6/5}$
$={(2^5)}^{6/5}=2^6=64$