Question

Let a and b 2 positive real number such that a

Answer 1

Proved

Explanation:

Given

Integers: a and b

Where
`a < b`

Required

Show that
`a^n < b^n`

We start by writing out the given expression

`a < b`

Then, take nth root of both sides

`a^n < b^n`

For instance:

Let a = 2, b = 2 and n = 4

First

Since
`2 < 3`

Then

`2^4 < 3^4`

`16 < 81`

Proved

This is so for all positive values of a,b and n where a < b