Lesson: Exponent Laws - Part I

Comment on Exponent Laws - Part I

The value of 12! is closest to:

A. (10^6)
B. 3(10^7)
C. 5(10^8)
D. 7(10^9)
E. 9(10^11)

Hi Brent,
I did not understand your approach to solve this question. What is 12!
Grateful for your help on this
gmat-admin's picture

Question link: https://gmatclub.com/forum/the-value-of-12-is-closest-to-233527.html

Good question, Fatima-Zahra.

In general, n! (read as "n factorial") is the product of all of the positive integers from 1 to n.

So, for example, 4! = 4 x 3 x 2 x 1
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
and 12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

More on factorial notation: https://www.gmatprepnow.com/module/gmat-counting/video/780


Hi Brent, could you explain how do we solve a factorial number in this case?
gmat-admin's picture

Sorry Jalal, but I'm not sure what you mean by "solve a factorial number."
If you mean how to evaluate (e.g., 3! = 6), then I cover that in my post here: https://gmatclub.com/forum/the-value-of-12-is-closest-to-233527.html#p18...


Hi Brent,

In the below DS question I know the answer is B but I failing to get a definite answer out of B. Need your help.

gmat-admin's picture

For (12^8)/(2^3)

can you do this?

(6^8)(2^8)/(2^3)= (6^8)(2^5)= 53,747,712?

gmat-admin's picture

You bet!

Rewriting 12^8 as (6^8)(2^8) is an application of the Combining Bases law (more here: https://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1029)

And simplifying (2^8)/(2^3)to get 2^5 is an application of the Quotient law.


HI Brent can u solve this question for me ? I am getting ans as Option D but ans = A HOW ?
2^(4−1)^2 /2^(3−2)=

A. 2^8
B. 2^7
C. 2^6
D. 2^5
E. 2^4
gmat-admin's picture

Question link: https://gmatclub.com/forum/2-104427.html

IMPORTANT: I'm adding some square brackets to show that we are squaring the value of (4-1)

We have: 2^[(4−1)^2]/2^(3−2)
Evaluate parts in bracket: 2^[(3)^2]/2^(1)
Evaluate again: (2^9)/(2^1)
Apply Quotient Law: 2^8

Answer: A


Hi Brent, will practicing problems given in this course suffice the quant need for GMAT? given the fact that I do not have quant background. Or should I practice from gmatclub as well https://gmatclub.com/forum/viewforumtags.php?
If I start practicing all the problems given in the link, it will take a lot of time to complete one single topic
gmat-admin's picture

For the most part, I believe there are enough practice questions in the Reinforcement Activities boxes beneath most video lessons.
Even if you were to answer only half of thos 420e linked practice questions, I believe that would be sufficient.
That said, GMAT Club is an excellent resource for extra questions.

If you find that this strategy will take too long, another approach is to keep answering practice questions within your target score range until you correctly answer 3 questions in a row. Doing so should demonstrate a reasonable mastery of that concept.

Yulia's picture

Hi Brent,


If x , p and q are positive integers , then x^p/x^q = ?
1. p = q + 5
2. x^q = 32

Could you please tell where I am making a mistake?

The question is x^(p-q) = ?
Statement 1: p = q + 5
p - q = 5
x^(p-q) = x^5, we don't know anything about x -> Insufficient

Statement 2: x^q = 32
x^q = 2^5
No info about q -> Insufficient

Both statement:
x^q = 2^5
x^(p-q) = x^5, no info to answer the question


x^p/x^q = x^p/32= x^p/2^5, still no info about ^p.
Answer is E.

Brent I have a separate question if we have x^p = 2^5 can we assume that base x is also 2?
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-x-p-and-q-are-positive-integers-then-22686...
Your reasoning/solution is perfectly valid.

Q: If we have x^p = 2^5 can we assume that base x is also 2?
No, If x^p = 2^5, it COULD be the case that x = 2 and p = 5, but it COULD also be the case that x = 32 and p = 1 (since 32^1 = 2^5 = 32)

Hey Brent,
I may have missed something, but do you reference the rules when raised to a negative exponent?

This is in reference to one of the reinforcement activities : 8^a*(1/4)^b = ?

I now understand the approach but want to familiarize myself with the theory. Thank you in advance!
gmat-admin's picture

Good catch! I shouldn't have that question here, since it requires knowledge of negative exponents (which happens to be the next video lesson after this one).
I've moved the question so that it's under the Negative Exponents lesson.
Thanks for the heads up.


Had to say that I got real panic when I saw this, and don't know what to do. my brain is like totally blank.

Even if I knew 81 is 3^4, I'm not sure what rule I can have, it seems like it's product law, but that's like completely new form to think about it...
gmat-admin's picture

Question link: https://gmatclub.com/forum/r-3-81-r-r-3-s-s-92651.html

It's a difficult question.
The more questions you see of this nature, the more accustomed you will be to finding the solution.

OK so for this question https://gmatclub.com/forum/is-7-x-100-1-7-x-2-9-800-2-7-2x-309930.html

I didn't modify anything (but it could be my own risks)

so the target question asks if x>3.

first one calculate if x = 2 or less then it CANNOT be greater than 9800 because I calculated it.

if the first one is correct, then second one makes sense because if x is 2 or less then it CANNOT be greater than 10000
gmat-admin's picture

Question link: https://gmatclub.com/forum/is-7-x-100-1-7-x-2-9-800-2-7-2x-309930.html

The original target question is "Is 7^x > 100?"
Rephrasing the target question to get "Is x > 3?" isn't quite right.
If x = 3, then 7^3 > 100, so, x = 3 is also allowed.

I'm not sure if I follow the rest of your solution.

OK, just went through your solution and understood.


I understand your solution***

Well, but I don't think I can perform it on the test day, i'm not that flexible and if I try to modify it then it can be the case that none of my modified version accordance with answer choices.
gmat-admin's picture

Question link: https://gmatclub.com/forum/the-value-of-12-is-closest-to-233527.html

If you're truly saying "I'm incapable of learning this new technique," then you might want to stick with performing all of the lengthy calculations.

no obviously I'm not..., I do learned this faster way, lengthy calculation is obviously not a good idea

OK so my one is not exactly like yours but could be right.

SO, 11*9 = 100, 12*8 =100, 7*5*3 = 100, 4*6*2*10 = 480

total = 480000000 = 5 * 10^8
gmat-admin's picture

Yes, there are several different ways we can approach this question.
Your approach is perfect. Great job!

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