# How is 20^5=(2^10 x 5^5) ??

#### prsndwg

7+ Year Member
How is it possible?

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

#### UCB05

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

#### baedero1

10+ Year Member
20^5 = (2*2*5)^5 = (2^2)^5*5^5 = 2^10*5^5

#### dfymarine

10+ Year Member
5+ Year Member
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!

#### whawha

10+ Year Member
how is it possible?

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

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

#### ongoingdat

5+ Year Member
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
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.

7+ Year Member
thank you alll

#### miedvied

7+ Year Member
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.

#### NumbaOneStunna

I can't tell if he's trollin...