Question

Simplify completely the quantity:

14 times x to the 5th power times y to the 4th power plus 21 times x to the third power times y to the 2nd power all over 7 times x to the third power times y

The equation and answer choices are attached.

Answer 1

perhaps it is A but I am not that sure

Answer 2

Answer:
2x²y³ + 3y which is the third option

Explanation:
Before we begin, remember the following:
xᵃ * xᵇ = x⁺ᵇ
$\frac{x^a}{x^b} = x^{a-b}$

The given expression is:
$\frac{14x^5y^4+21x^3y^2}{7x^3y}$

1- We can take 7x³y as a common factor from both terms in the numerator.
Following second rule mentioned above, this will give us:
$\frac{7x^3y(2x^2y^3+3y)}{7x^3y}$

2- Now, we can note that 7x³y can be cancelled from both the numerator and the denominator.
Doing this, we will end up with the following:
2x²y³ + 3y

Hope this helps :)