solve for a: a^3b/4=7/vc^2

Question

Need to simplify this equation and solve for 'a'

Answer 1

a^3 b  =    7                   .
  4           v c^2

Brian is right in his steps... just thought you would like to see what is happening with each of those steps:

The object is to get the variable, a, alone.  So let's take care of the denominator first by multiplying both sides of the equation by 4:

4 •    a^3 b   =     4 •    7              .
           4                    v c^2  

See how the 4's cancel on the left side?  And on the right hand side, you end up with a 28 in the numerator:  

 a^3 b    =     28                  .
                   v  c^2 

Now, we still have a b "bothering" the a-term, so we have to divide both sides by b (or you can say multiply both sides by 1/b)...

1  •   a^3  b   =    1   •    28                          .
b          1              b      v c^2

The b's cancel on the left side, and we are left with:

a^3  =     28                       .
            b v c^2

Lastly take the third root on both sides (3√ )... 

And yes, we get the same answer as Brian:

a = 3√ (   28       )
           (  b v c^2 )

Sorry for the poor math editing here.

Hope this helps you see the steps better.

Answer 2

Times both sided by 4, then divide both sides by "b" and lastly take the cube root of both sides.

a = (28/bvc^2)^1/3