For this case we have the following expressions:
[tex]45^{10} * 5^ {40}[/tex] and [tex]25^{20}[/tex]
Let:
[tex]45^{10} * 5^ {40}[/tex] (Integer m)
[tex]25^{20}[/tex] (Integer n)
By definition, an integer m is divisible by an integer n if the remainder of the division is 0. That is, there is an integer p such that: [tex]m = n * p[/tex]
Rewriting the expression we have:
[tex]25^{20} = 5^{2 * (20)} = 5^{ 40}[/tex]
So:
[tex]\frac {45^{10} * 5^{ 40}} {5^{40}} =[/tex]
We cancel similar terms:
[tex]45^{10}[/tex]
We check:
[tex]45^{10} * 5^{ 40} = 5^{ 40} * 45^{ 10}[/tex]
Answer:
If they are divisible
