# How do you simplify #m^5/m^2# and write it using only positive exponents?

##### 2 Answers

#### Explanation:

#m^5/m^2=(mxxmxxmxxmxxm)/(mxxm)#

#color(white)(m^5/m^2)=(cancel(m)xxcancel(m)xxmxxmxxm)/(cancel(m)xxcancel(m))larr" cancelling"#

#color(white)(m^5/m^2)=m^3#

#"this result can be expressed generally as"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(a^m/a^n=a^((m-n)))color(white)(2/2)|)))#

#rArrm^5/m^2=m^((5-2))=m^3#

#### Explanation:

Before we just blindly apply a rule, let's look at what we we have and what it actually means.

We know that anything divided by itself is

so each time we have

Both the

This leads us to the rule for dividing with indices:

Here is another example for clarity.