Answer:
Proved
Step-by-step explanation:
Given
Integers: a and b
Where [tex]a < b[/tex]
Required
Show that [tex]a^n < b^n[/tex]
We start by writing out the given expression
[tex]a < b[/tex]
Then, take nth root of both sides
[tex]a^n < b^n[/tex]
For instance:
Let a = 2, b = 2 and n = 4
First
Since [tex]2 < 3[/tex]
Then
[tex]2^4 < 3^4[/tex]
[tex]16 < 81[/tex]
Proved
This is so for all positive values of a,b and n where a < b
