Question

Please help!! 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? _______

Answer 1

Answer:

The value of a is: 0

Step-by-step explanation:

We are given a expression by:

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.

which is mathematically written as:

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

Now, this expression could also be written as:

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

Since,

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

Now, on further simplifying we have:

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

since,

$\dfrac{x^m}{x^n}=x^{m-n}$

Hence, we have :

$=2x^0y^1+4x^1y^3$

Hence, on comparing it with:

$2x^ay^b+4x^cy^d$

we have:

$a=0,\ b=1\ ,\ c=1\ and\ d=3$

Answer 2

You want the exponent of x in the first term of ...

$\dfrac{4xy^3+8x^2y^2}{2xy^2}=\frac{4}{2}x^{(1-1)}y^{(3-2)}+\frac{8}{2}x^{(2-1)}y^{(2-2)}\\\\=2x^0y^1+4x^1y^0$

The exponent a is 0.