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
Fatima-Zahra
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

Cheers,
Brent

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...

Cheers,
Brent

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.

https://gmatclub.com/forum/is-5-k-less-than-144719.html
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.

Cheers,
Brent

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

Cheers,
Brent

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