Question

Find the product: $a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)$

Answer 1

Simplify using the rules of exponents:

The given expression is $a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)$.

It can be simplified as follows,

$a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)=a^2\times 2\times a^{22}\times 4\times a^{26}$

$\Rightarrow a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)=2\times 4\times a^2\times a^{22}\times a^{26}$

$\Rightarrow a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)=8\times a^{2+22+26}$ $\left[\because a^m\times a^n=a^{m+n}\right]$

$\Rightarrow a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)=8\times a^{50}$

$\Rightarrow a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)=8a^{50}$

Hence, the value of the product $a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)$ is $8a^{50}$.