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

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prsndwg

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How is it possible?

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

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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!
 
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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.
 
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.
 
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