If the quantity 4 times x times y cubed plus 8 times x squared times y to the fifth power all over 2 times x times y squared is completely simplified to 2xayb + 4xcyd, where a, b, c, and d represent integer exponents, what is the value of a?

Question

Unnecessary · Answer

Any ideas?

AZ · Answer

We want to simplify the left side so that way we can find out what the exponents on 'x' and 'y' are on the right side

AZ · Answer

$\Large\dfrac{4xy^3 + 8x^2y^5}{2xy^2} = 2x^{a}y^{b} + 4x^{c}y^{d}$

AZ · Answer

There's a few rules you need to know

$ \dfrac{a+b}{c} = \dfrac{a}{c} + \dfrac{b}{c}$

AZ · Answer

so knowing that, we can re-write

$\large\dfrac{4xy^3 + 8x^2y^5}{2xy^2} $

as

$\large\dfrac{4xy^3}{2xy^2} + \dfrac{8x^2y^5}{2xy^2} $

and so now here's an exponents rule that you should know

$\large \dfrac{a^b}{a^c} = a^{b-c}$

Can you simplify it further?

how would you divide $\dfrac{4xy^3}{2xy^2}$

just do it part by part

what is 4/2 = ?
what is x/x = ?
what is $\dfrac{y^3}{y^2} = ?$