# Lesson: Exponent Laws - Part II

## Comment on Exponent Laws - Part II

### I love the fact that you have

I love the fact that you have collated many questions from various forums into one place. This is by far the best collection of questions that keep a student engaged within the GMAT community. Would like to see a lot more questions. Thanks! We're adding questions every day.

### Hi Brent.

Hi Brent.

https://gmatclub.com/forum/if-5-13-9-7-3-15-x-what-is-the-value-of-x-219722.html

We can answer this question by keeping track of the 5's only.
Given: (5^13)(9^7)=3(15^x)
Rewrite as: (5^13)(9^7)=3(5^x)(3^x)
So, it must be true that (5^13) = (5^x)
So, x = 13 Good question.
When I get to (5^13)(9^7)=3(5^x)(3^x), I can see that, if I were to write the LEFT side of this equation as the product of 5's and 9's, I'd have THIRTEEN 5's and SEVEN 9's.

Likewise, I were to write the RIGHT side as the product of 5's and 3's, I'd have x 5's and (x+1) 3's.

Since the left side EQUALS the right sides, it must be the case that we have the same number of 5's on each side.
In other words, it must be true that x = 13

Does that help?

Cheers,
Brent

### Hey Brent,

Hey Brent,

I am trying to solve the following question:

If (1/5)^m * (1/4)^18 = 1/(2(10))^35 , then m =

17

18

34

35

36.

I have simplified the right side to 1/2 * 10^(-35) but I cannot figure out how to proceed. I've looked through the videos but can't finde a suitable one. Any solutions and video recommendations on this topic are greatly appreciated.

Cheers,
Kevin ### Thank you Brent, as always

Thank you Brent, as always much appreciated!

### Hello Brent,

Hello Brent,

If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

Given d= 1/(2^3*5^7) i

Multiply by 2^4/ 2^4
d=2^4/(2^3∗5^7)∗2^4=
2^4/ 2^7 ∗ 5^7 =
2^4/ 10^7 = 16 / 10^7 = 0.0000016
Hence D will have two non-zero digits, 16, when expressed as a decimal.

I have a question concerning the solution, why do we ignore the multiplication of 2^4 x 5^7 ?

Thank you ### Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/if-d-1-2-3-5-7-is-expressed-as-a-terminating-...