Question

Product of two expressions is $8s^3{t}^2$. If one of the expression is $2st$, then the other expression is

• A. $4s^{2}t$
• B. $8s^{2}t$
• C. $4s^3{t}^2$

Answer 1

The correct option is A $4s^{2}t$

Let two quantities be $a$ and $b$.
Product of two quantities is $8s^3{t}^2$.
$\Rightarrow$ $a\times b=8s^3{t}^2$
$\Rightarrow$ $b=\frac{8s^3{t}^2}{a}$
Say, $a=2st$
Substituting $a$ in the above equation we get,
$b=\frac{8s^3{t}^2}{2st}=\frac{2\times 4s^3{t}^2}{2\times st}$
Canceling the common term and substracting the exponent of respective unknowns we get,
$b=4\times s^{(3-1)}\times t^{(2-1)}=4s^{2}t$