The value of $9^{\frac{1}{3}} imes 9^{\frac{1}{9}} imes 9^{\frac{1}{27}} imes \ldots\infty$ is

Question

The value of $9^{\frac{1}{3}} 	imes 9^{\frac{1}{9}} 	imes 9^{\frac{1}{27}} 	imes \ldots\infty$ is

Dr. Abubacker · Accepted Answer

(c)
$9^{\frac{1}{3}} 	imes 9^{\frac{1}{9}} 	imes 9^{\frac{1}{27}} 	imes \ldots\infty = (9)^{\left\lbrack \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + ...\infty ightbrack}$
$= (9)^{\frac{1}{3}\left( \frac{1}{1 - \frac{1}{3}} ight)} = 9^{\frac{1}{2}}$
$= 3$

Q. The value of $9^{\frac{1}{3}} \times 9^{\frac{1}{9}} \times 9^{\frac{1}{27}} \times \ldots\infty$ is

Explanation

Reviewed by Dr. Abubacker

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