The Zero Exponent Rule

Please watch the video to understand the Zero Exponent Rule.

$\displaystyle {x}^{{0}}={1}$, where $\displaystyle {x}\ne{0}$

If the base is not zero, and the exponent is zero, the answer 1.

 

Here's the reason why this makes sense. Suppose I have $\displaystyle \frac{{5}^{{3}}}{{5}^{{3}}}$, using the quotient rule this is $\displaystyle {5}^{{{3}-{3}}}={5}^{{0}}$. I can also think of what happens when I simplify this like a fraction $\displaystyle \frac{{5}^{{3}}}{{5}^{{3}}}=\frac{{125}}{{125}}={1}$.

$\displaystyle {x}^{{0}}=\frac{{x}^{{n}}}{{x}^{{n}}}={1}$ as long as $\displaystyle {x}$ isn't zero (we cannot divide by zero).

Complete this expression. Assume that any variables are not equal to zero.
$\displaystyle {z}^{{0}}$= Preview Question 6 Part 1 of 4  

Simplify the following expression completely.
$\displaystyle {\left({4}{v}+{2}\right)}^{{0}}$ = Preview Question 6 Part 2 of 4  

Simplify the following.
$\displaystyle {3}^{{0}}$ = Preview Question 6 Part 3 of 4  

Note: $\displaystyle {0}^{{0}}$ is undefined. $\displaystyle {0}^{{n}}={0}$ for any exponent $\displaystyle {n}\ne{0}$.
Simplify. $\displaystyle {0}^{{5}}$ = Preview Question 6 Part 4 of 4