Help answer 3 questions from GMATPrep

[alflauren]

Here are three questions from a practice GMAT. I have included the question stem with the answer, but I want to know why each of the questions are correct. (i.e. why m=35, why that big equation=16 if xy=1, and why that function of x is the right one.) I would really appreciate your help with figuring out the process on each of these! (questions attached)

[hangptt]

Q2: 2^(x+y)^2 / 2^(x-y)^2 = 2^ (x+y)2-(x-y)^2 = 2^4xy=2^4=16

Q3: though you don't post whole question, I extract from the right answer as follows:
f(x)=x^2(1-x)^2

=> f(1-x) = (1-x)^2 (1-1+x)^2 = x^2 (1-x)^2

since (1-x)^2=(x-1)^2 then f(x) = f(1-x)

[manish8109]

Q1) 1/5^m * 1/4^18 = 1/2 *1/10^35

=> 1/5^m * 1/2^36 = 1/2 * 1/10^35
=> 1/5^m *1/2 * 1/2^35 = 1/2 * 1/5^35 * 1/2^35

comparing both sides

1/5^m = 1/5^35
=> m=35(answer)

[alflauren]

Can someone tell me why 1/2^36 = 1/4^18 ?

What is the method of operation that lets you change 2^36 to 4^18? Can you do that with any other bases, or only 2, 4, 8, etc?

Thanks!

[manish8109]

Aflauren,

(a^b)^x = a^(bx)

so, 4^18 = (2^2)^18= 2^36

thanx

[alflauren]

Oh, friggin' A. That's just too easy. Thank you.

[T-REX]

Yeah it's Indices. I just pulled up a 8th Class book and solved some of them it really helps..