Jun 14, 2009
800
3
Status
Pre-Dental
How is it possible?

20^5=(2^10 x 5^5) ???!!
20^5
= 20 x 20 x 20 x 20 x 20
= (2x2x5) x (2x2x5) x (2x2x5) x (2x2x5) x (2x2x5)
= (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)(5 x 5 x 5 x 5 x 5)
= 2^10 x 5^5
 

dfymarine

10+ Year Member
5+ Year Member
Jan 3, 2007
134
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Pre-Dental
20^5
= 20 x 20 x 20 x 20 x 20
= (2x2x5) x (2x2x5) x (2x2x5) x (2x2x5) x (2x2x5)
= (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)(5 x 5 x 5 x 5 x 5)
= 2^10 x 5^5

UCB05, you are indeed the DAT MACHINE!
 

ongoingdat

5+ Year Member
Jun 29, 2009
84
0
Status
Dental Student
How is it possible?

20^5=(2^10 x 5^5) ???!!
(2 x 5 x 2)^5 = 2^5 x 5^5 x 2^5 = 5^5 x 2^10.

You add exponential together when you have same thing like (2).
So you simply add 5 + 5 and write it as 2^10.
 

joonkimdds

Senior Member
10+ Year Member
7+ Year Member
Jun 30, 2005
2,780
2
Status
Pre-Dental
How is it possible?

20^5=(2^10 x 5^5) ???!!
(AB)^2 is same as (A^2 x B^2)

also, 2^10 is same as [2^2]^5 which is same as 4^5
thus as soon as I see 20^5, I will want to make it into (4x5)^5 which is same as (4^5 x 5^5) which is same as 2^10 x 5^5.

I know that I made it sound like it's very complicated but it's actually super simple.
 

miedvied

7+ Year Member
Apr 23, 2009
146
1
Status
Pre-Dental
How is it possible?

20^5=(2^10 x 5^5) ???!!

I went the shorter way here:

(20)^5
(4*5)^5
(2^2 *5^1) ^5
2^10 * 5^5

When you apply an exponent to an exponent, they multiply - so opening the parenthesis on two to the second will multiply the exponent 2 by five, and the exponent one by five.