# How do you simplify  5m^0?

May 25, 2016

5

#### Explanation:

$\textcolor{g r e e n}{\text{Note that you are 'not allowed' to divide by 0}}$
$\textcolor{g r e e n}{\text{So "x/x=0/0 !=1" It is 'undefined' (not allowed)}}$

Consider $\frac{4}{4} = 1$ now compare that to $\frac{x}{x} = 1$

Considering the same thing but by using powers

$\textcolor{b r o w n}{\text{If you have "1/x" you can write this as } {x}^{- 1}}$
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Now think about $x \times x = {x}^{2}$

But $x$ can be written as ${x}^{1}$

So $x \times x = {x}^{2} \to {x}^{1} \times {x}^{1} = {x}^{2}$

$\textcolor{b r o w n}{\text{So } {x}^{1} \times {x}^{1} = {x}^{1 + 1} = {x}^{2}}$
'.............................................................
$\textcolor{b l u e}{\text{Putting it all together}}$

So if we have $\frac{x}{x}$ this can be written as

$x \times \frac{1}{x}$

$= {x}^{1} \times {x}^{- 1}$

$= {x}^{1 - 1}$

$= {x}^{0} = 1$
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$\textcolor{b l u e}{\text{Answering your question}}$

Thus ${m}^{0} = 1$ so $5 {m}^{0} = 5 \times 1 = 5$