Question

Simplified form of $\frac{8^{3a}\times 2^5\times 2^{2a}}{4\times 2^{11a}\times 2^{-2a}}$ is $2^{2a+k}$
then the value of $k$ is

Answer 1

$\frac{8^{3a}\times 2^5\times 2^{2a}}{4\times 2^{11a}\times 2^{-2a}}$

$=\frac{(2^3{)}^{3a}\times 2^5\times 2^{2a}}{\left(2^2\right)\times 2^{11a}\times 2^{-2a}}$

$=\frac{(2{)}^{9a}\times 2^5\times 2^{2a}}{2^2\times 2^{11a}\times 2^{-2a}}$

$=\frac{2^{9a+5+2a}}{2^{2+11a-2a}}$

$=\frac{2^{11a+5}}{2^{9a+2}}$

$=2^{11a+5-9a-2}$

$=2^{2a+3}$