When you divide a base with an exponent by a base with an exponent, you subtract the exponents together. (But you can only combine exponents when the bases are the same)
For example:
[tex]\frac{x^5}{x^2} =x^{(5-2)}=x^3[/tex]
[tex]\frac{x^2}{y^4}[/tex] (You can't combine them as they have different bases of x and y)
[tex]\frac{w^9}{w^7} =w^{(9-7)}=w^2[/tex]
When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.
For example:
[tex]x^{-3}[/tex] or [tex]\frac{x^{-3}}{1} =\frac{1}{x^3}[/tex]
[tex]\frac{1}{y^{-3}} =\frac{y^3}{1}[/tex] or [tex]y^3[/tex]
[tex]\frac{27mn^3}{51m^6n}[/tex] You can simplify the whole fraction or just "m" since you need to find the exponent of "m". I will simplify the whole fraction.
[tex]\frac{27}{51} *m^{(1-6)}*n^{(3-1)}[/tex]
[tex]\frac{9}{17} *m^{-5}*n^2[/tex] Make all the exponents positive
[tex]\frac{9n^2}{17m^5}[/tex] So the exponent of m = 5, your answer is the 3rd option
