Question

What would be the missing values for this

Answer 1

Given:

$x^{2} y^{8} \cdot \frac{x^{3} y^{?}}{x y^{3}}=x^{4} y^{2}$

To find:

The missing value.

Solution:

Let the missing value be m.

$x^{2} y^{8} \cdot \frac{x^{3} y^{m}}{x y^{3}}=x^{4} y^{2}$

Using exponent rule: $a^m \cdot a^n=a^{m+n}$

$\frac{x^{2+3} y^{8+m}}{x y^{3}}=x^{4} y^{2}$

$\frac{x^{5} y^{8+m}}{x y^{3}}=x^{4} y^{2}$

Using exponent rule: $\frac{a^m}{a^n} =a^{m-n}$

$x^{5-1} y^{8+m-3}=x^{4} y^{2}$

$x^{4} y^{5+m}=x^{4} y^{2}$

Equate x terms and y terms.

$x^4=x^4$ and $y^{5+m}=y^2$

If the bases are same, then the powers are equal.

$5+m=2$

Subtract 5 from both sides.

$5+m-5=2-5$

$m=-3$

The missing value is -3.