Answer:
32
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