# What is the zero exponent rule such as x^3/x^3?

Jul 9, 2016

${x}^{3} / {x}^{3} = {x}^{0} = 1$

#### Explanation:

Any number to the power of 0 is equal to 1.

${x}^{3} / {x}^{3}$ can be calculated in two ways:

Method 1. Cancel because $\text{anything"/"itself} = 1$

$\frac{6}{6} = 1 , \text{ } \frac{- 8}{- 8} = 1$ etc

${\cancel{{x}^{3}}}^{1} / {\cancel{{x}^{3}}}^{1} = 1$

Method 2: Using laws of indices,:
${x}^{3} / {x}^{3} = {x}^{3 - 3} = {x}^{0}$

However there can only be one answer, which means that the two answers from the different methods have to mean the same thing.

:. ${x}^{3} / {x}^{3} = {x}^{0} = 1$