Question

How do you solve `x^(-3/5) = 1`?

Answer 1

`x=1`

Explanation:

We can use some rules to find out.

First rule we'll use is `x^-1=1/x`:

`x^(-3/5)=1`

`1/(x^(3/5))=1/1`

We can invert both sides:

`x^(3/5)/1=1/1=>x^(3/5)=1`

Now to the exponent. We're asked to cube `x` (that's the 3) and also take the 5th root.

With odd exponents, sign is preserved. What I mean by that is that when we have `(-1)^2`, we end up with 1. Same with `(-1)^4, (-1)^6` and all other even exponents. Not so with `(-1)^3, (-1)^5` and all other odd exponents - we end up with `-1`.

What this means is that `x=1` but it can't equal `-1`.

Here's a graph to show the solution:

graph{(y-x^-(3/5))((x-1)^2+(y-1)^2-.1)=0}