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

Oct 16, 2015

${x}^{0} = 1$.

#### 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": ${x}^{- 5} = \frac{1}{{x}^{5}}$.

So, ${x}^{- 5} \cdot {x}^{5} = \frac{1}{{x}^{5}} \cdot {x}^{5} = 1$

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,

${x}^{- 5} \cdot {x}^{5} = {x}^{- 5 + 5} = {x}^{0} = 1$.