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)

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