Question

How do you rewrite `x^-5 x^5` using a positive exponent?

Answer 1

`x^0=1`.

Explanation:

Actually, `x^{-5}` is exactly the inverse number of `x^5`, assuming `x ne 0`. In fact, a negative power means "`1` over the positive power": `x^{-5}=1/{x^5}`.

So, `x^{-5}*x^5 = 1/{x^5}*x^5 = 1`

Obviously, `1=x^0` (any number to the power of zero is one, as long as the number is different from zero).

Also, using the power multiplication rule, we can work this way: you multiplicate powers of the same number by adding the exponents. In this case,

`x^{-5}*x^5=x^{-5+5}=x^0=1`.