Question

Find the value of $7ab\times 4ab\times 2ab$.

• A. $28a^2{b}^2$
• B. $56a^2{b}^2$
• C. $28a^3{b}^3$
• D. $56a^3{b}^3$

Answer 1

The correct option is D $56a^3{b}^3$

$\underset{–}{Step1:}$

First, we would multiply $7ab$ and $4ab$. This product can be evaluated as:
$\left(7ab\right)\times \left(4ab\right)$

$=(7\times 4)\times (ab\times ab)$

$=28\times \left(a^{1+1}{b}^{1+1}\right)$ $(\because a^m\times a^n=a^{m+n})$

$=28\times a^2{b}^2$


The value of the product $\left(7ab\right)\times \left(4ab\right)$ is $28a^2{b}^2$.


$\underset{–}{Step2:}$

Now, we would multiply $28a^2{b}^2$ with $2ab$. This product can be evaluated as:
$7ab\times 4ab\times 2ab$
$=(7ab\times 4ab)\times 2ab$
$=\left(28a^2{b}^2\right)\times \left(2ab\right)$
$=(28\times 2)\times (a^2{b}^2\times ab)$

$=56\times \left(a^{2+1}{b}^{2+1}\right)$ $(\because a^m\times a^n=a^{m+n})$

$=56a^3{b}^3$

$7ab\times 4ab\times 2ab=56a^3{b}^3$

The value of the product $7ab\times 4ab\times 2ab$ is $56a^3{b}^3$. Therefore, option (d.) is the correct answer.