this is the hardest thing ever! help...?

Question

(2x^(3 / 2) + (4x)^(3 / 2)) / (5x^(- 3 / 4))

Answer 1

It would simplify to: [ 2x^(9/4) + 8x^(9/4)]/5
equals 2x^(9/4)

Answer 2

Remember that you only add exponents when you are multiplying or subtract when you are dividing.

In order to add the first 2 terms you need to make sure that they have the same exponents which they have:
Example: x^2 + x^2 = 2x^2

Numerator: 2x^(3/2) + 4x^(3/2) = 6x^(3/2)

Now you have:

6x^(3/2) / 5x^(-3/4)

--> you have a division (we subtract exponents)

(3/2) - (-3/4) = 3/2 + 3/4

You need the same denominator in order to add.
Denominator is 4

6/4 + 3/4 = 9/4 ---> This is your new exponent for X

Solution: (6/5)x^(9/4)

Answer 3

= 2x^3/2 + [(4x)^(3/2)] / [5x^(-3/4)]
= 2x^3/2 + [8x^(3/2 - (-3/4))] / 5
= 2x^3/2 + [8x^(9-4)] /5

Answer 4

Is that supposed to equal something?