This question is from the GMAT PREP- Answer 35.

What is the best to about solving this problem-

(1/5)^m (1/4)^18= 1/2(10)^35

the right side of your notation is ambiguous: a strict order-of-operations interpretation would place the (10)^35 in the numerator. obviously, though, everything is in the denominators, so let's proceed from there.

- recognizing the way fractions multiply, we can see that everything will just stay in the denominators. therefore, we can just pay attention to the denominators, obviating the need to use actual fractions:
(5^m)(4^18) = 2(10^35)

as is par for the course with problems like this, we need to look at the prime factorizations of the two sides of the equation.
- the right side contains 36 twos and 35 fives (each '10' is a two and a five)
- the left side contains 36 twos and "m" fives (each '4' is 2 twos)
so m = 35.

don't be intimidated by problems like this one (although they do, admittedly, look spooky). just start thinking about prime factors and you should be well on your way to solutionville.

OMG I love you RPurewall. I'm on my way to Stanford!

I would Get everything to powers of prime numbers on both sides.

(1/5)^m (1/4)^18= 1/2(10)^35

rewrite as

5 ^ -m x 2 ^ -36 = 2 ^ -1 x 2 ^ -35 x 5 ^ -35

compare powers for 2 and 5 which gives (-m) = (-35) and (-36) = (-1) + (-35)

thanks!

sweetness.

Saurav: My question relates to the right side of the equation as presented by you -- How does 10^35 in the original equation translate into 2 ^ -35 x 5 ^ -35 -- in yours? I would imagine that 10^35 would equal 2^+35 * 5^+35.

he's pulling that out of the denominator and using a negative power; if you're confused, you're confused because he's doing this at the same time as he's breaking the 10 up into 5 x 2.

--

note, though, that there's no reason to bother with the negative powers, since everything in this problem is in the denominators. you can just take all of it, and ignore the denominators entirely; i.e., if 1/a * 1/b = 1/c, this just means that a * b = c.

see the second post in this thread.