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# Find the geometric mean of 5 numbers 2, 8, 16, 128, 512

$\begin {array} {1 1} (A)\;2 & \quad (B)\;2^{\large\frac{24}{5}} \\ (C)\;2^{\large\frac{4}{5}} & \quad (D)\;None\: of \: these \end {array}$

Ans : (B)
Geometric mean = $( 2 \times 8 \times 16 \times 128 \times 512 )^{\large\frac{1}{5}}$
$= ( 2^1 \times 2^3 \times 2^4 \times 2^7 \times 2^9) ^{\large\frac{1}{5}}$
$= (2^{1+3+4+7+9})^{\large\frac{1}{5}}$
$= 2^{\large\frac{24}{5}}$