SOLUTION: sqrt(8a^9)/b^3 = (8a^9)(b^3) = (8a^3)(b^3) = 8ab^3 Is this correct? I am not sure I am following the steps correctly in this formula?

Algebra ->  Square-cubic-other-roots -> SOLUTION: sqrt(8a^9)/b^3 = (8a^9)(b^3) = (8a^3)(b^3) = 8ab^3 Is this correct? I am not sure I am following the steps correctly in this formula?       Log On


   

Question 241289: sqrt(8a^9)/b^3 = (8a^9)(b^3)

= (8a^3)(b^3)
= 8ab^3
Is this correct? I am not sure I am following the steps correctly in this formula?
Thanks.
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:

sqrt%288a%5E9%29%2Fb%5E3+=+%288a%5E9%29%2A%28b%5E3%29

since b^3 * b^3 = b^(3+3), then multiply both sides of equation by b^3 to get:


sqrt%288a%5E9%29+=+%288a%5E9%29%2A%28b%5E6%29

divide both sides of your equation by b^9 to get:

%28sqrt%288a%5E9%29%29+%2F+%288a%5E9%29+=+%28b%5E6%29

since sqrt(8a^9)^2 = 8a^9, and (8a^9)^2 = 64a^18, and (b^6)^2 = b^12, then square both sides of your equation to get:

%288a%5E9%29+%2F+%2864a%5E18%29+=+%28b%5E12%29

since 8/64 = 1/8, and a^9 / a^18 = a^(9-18) = a^(-9) = 1/a^9, then perform the indicated operations to get:

%281%2F%288a%5E9%29%29+=+%28b%5E12%29

if you are solving for b, then you will get:

b+=+root%2812%2C%281%2F%288a%5E9%29%29%29

if you are solving for a, then you will get:

a+=+root%289%2C%28%281%2Fb%5E12%29%2F8%29%29

I confirmed the answer is good by letting a = 2.

This made b = .5

You can confirm for yourself by using any number for a and then solving for b.

conversely you can use any number for b and then solve for a.

either way, the answers should be able to be plugged into the original equation to confirm that the values are good.







Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Exactly what is the problem?
You have 2 expressions that are equal? Or is that work you did on it?