3asqrd over 5bsqrd divided by sqr root 9asqrd over 100bsqrd

How the **** do I do this Im going to fail my maths exam :/ the answer is 2a over b

No sweat. Let's go step by step.

(3a^2 / 5b^2) / sqrt(9a^2 / 100b^2)

First, let's evaluate the square root.

(3a^2 / 5b^2) / (3a / 10b)

Now you have a big fraction with a fractional numerator and a fractional denominator. You're going to pull that fractional demoninator out, invert it, and then multiply it by the fractional numerator. Like this:

(3a^2 / 5b^2) * (10b / 3a)

When you have two fractions multiplied, you can cancel out stuff from the numerator and denominator. For example, the 3 coefficient cancels, so you get:

(a^2 / 5b^2) * (10b / a)

Then, you can factor 5 out of the 5b^2 and 10b terms. So you get:

(a^2 / b^2) * (2b / a)

Then, you can factor a out of the a^2 and a terms. So you get:

(a / b^2) * (2b / 1)

Finally, you can factor b out of the b^2 and 2b terms. So you get:

(a / b) * (2 / 1)

Now, just multiply your fractions to get your final answer.

(2a / b)

There's your answer. Good luck on your exam. :-)

the first thing you need to do is get rid of the square root so 9 is 3*3 a^2 is a*a so you have 3a. 100 is 10*10 and b^2 is b*b so you get 10b so the fraction you are dividing by is 3a/10b when you divide by a faction you multiply by the reciprocal of the second fraction so 3a^2/5b^2 is times10b/3a, multiply out to get 3*2*5*a*a*b all over 5*3*b*b*a cancel things that are the same in both fractions. The 3,5,a,b so you are left with 2a over b.

I think you answered your own question.