Question

Hey guys how do you simplify this fully?​

Answer 1

Answer:

32

Step-by-step explanation:

In 100^1000,

100 can be written as,

100 = 10 x 10 = 10^2

100^1000

= 10^( 2 * 1000 )

= 10^2000

10 can be written as,

10 = 2 x 5

10^2000

= ( 2 x 5 )^2000

Formula : -

( a x b )^n = a^n x b^n

Here,

a = 2

b = 5

n = 2000

( 2 x 5 )^2000 = 2^2000 x 5^2000

[ 2^2005 x 5^2000 ] / 100^1000

= [ 2^2005 x 5^2000 ] / [ 2^2000 x 5^2000 ]

Formula : -

a^m x b^n / a^c x b^d

= a^( m - c ) x b^( n - d )

Here,

a = 2

m = 2005

c = 2000

b = 5

n = d = 2000

[ 2^2005 x 5^2000 ] / [ 2^2000 x 5^2000 ]

= 2^( 2005 - 2000 ) x 5^( 2000 - 2000 )

= 2^5 x 5^0

{ Note : Any number power 0 ( except 0 ) is 1.

That is 0^0 ≠ 1, but 5^0 = 1. }

= 2^5 x 1

= 2^5

= 2 x 2 x 2 x 2 x 2

= 32