How do you simplify #((4a^3 b)/(a^2 b^3)) ((3b^2)/(2a^2 b^4))#?
First of all, you can simplify each fraction on its own: to make things easier to see, you can rewrite the first fraction as a multiplication of three fractions, each involving only one variable, or the numeric part:
Now you can simplify exponents:
We can do the same for the second fraction:
We can simplify exponents on the
So, the multiplication between the two fraction has become
As a final step, we can cross simplify factor, which means that we can simplify the same factors if they appear at the numerator of one fraction and the denominator of the other. In our case, we have