Question

Which values of a and b make the equation true?

Answer 1

Answer:

The values of a and b are a=3 and b=3.

Step-by-step explanation:

Given fractional equation is $\frac{(2xy)^4}{4xy}=4x^ay^b$

To find the values of   a and b to make given equation true :

$\frac{(2xy)^4}{4xy}=4x^ay^b$

Take LHS $\frac{(2xy)^4}{4xy}$

$=\frac{2^4x^4y^4}{4xy}$ ( using the property $(ab)^m=a^mb^m$ )

$=\frac{16x^4y^4}{4xy}$

$=4x^4y^4x^{-1}y^{-1}$ ( using the property $\frac{1}{a^m}=a^{-m}$ )

$=4x^{4-1}y^{4-1}$ ( using the property $a^m.a^n=a^{m+n}$ )

$=4x^3y^3$

$\frac{(2xy)^4}{4xy}=4x^3y^3$

Comparing with $\frac{(2xy)^4}{4xy}=4x^ay^b=4x^3y^3$

Therefore $4x^ay^b=4x^3y^3$

Therefore the values of a and b are a=3 and b=3