Question

Prove the divisibility of the following numbers: 45^10·5^40 by 25^20

Answer 1

For this case we have the following expressions:

$45^{10} * 5^ {40}$ and $25^{20}$

Let:

$45^{10} * 5^ {40}$ (Integer m)

$25^{20}$ (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: $m = n * p$

Rewriting the expression we have:

$25^{20} = 5^{2 * (20)} = 5^{ 40}$

So:

$\frac {45^{10} * 5^{ 40}} {5^{40}} =$

We cancel similar terms:

$45^{10}$

We check:

$45^{10} * 5^{ 40} = 5^{ 40} * 45^{ 10}$

Answer:

If they are divisible