Question

If \[\dfrac{{4a{b^2}( - 5a{b^3})}}{{10{a^2}{b^2}}}\; = - K{b^3}\;\] then value of K is ___.

Answer 1

Hint: To get the value of K in this problem we just have to solve the given expression in terms of k then cancel out the like terms from LHS and RHS such that we can find the value of k as it is asked in the question.

Complete step-by-step answer:
Given,
\[\dfrac{{4a{b^2}( - 5a{b^3})}}{{10{a^2}{b^2}}}\; = - K{b^3}\;\]
Or we can simplified the above expression
Like,
\[\Rightarrow \dfrac{{4 \times - 5}}{{10}} \times \dfrac{{a{b^2} \times a{b^3}}}{{{a^2}{b^2}}} = - K{b^3}\]
On cancelling out the like terms we get a simplified expression as written below.
\[\Rightarrow \dfrac{{ - 20}}{{10}} \times {b^3} = - K{b^3}\]
Now cancelling the b3 we get,
 \[ - 2 = - K\]
Now multiplying -1 both side we get the value of k
$K = 2$
So, the correct answer is “ k=2”.

Note: This is quite a simple question just we have to cancel out the like terms and find the value of K, while students may get wrong on cancelling the like terms while cancelling the like terms just be careful. Make sure you correctly multiply the powers of like terms else the obtained answer will be wrong.