Question

Which of the following functions is reduced what will be the exponent on the M 27mn^3/51m^6n

Answer 1

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:

$\frac{x^5}{x^2} =x^{(5-2)}=x^3$

$\frac{x^2}{y^4}$    (You can't combine them as they have different bases of x and y)

$\frac{w^9}{w^7} =w^{(9-7)}=w^2$

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:

$x^{-3}$ or $\frac{x^{-3}}{1} =\frac{1}{x^3}$

$\frac{1}{y^{-3}} =\frac{y^3}{1}$ or $y^3$    

$\frac{27mn^3}{51m^6n}$      You can simplify the whole fraction or just "m" since you need to find the exponent of "m". I will simplify the whole fraction.

$\frac{27}{51} *m^{(1-6)}*n^{(3-1)}$

$\frac{9}{17} *m^{-5}*n^2$      Make all the exponents positive

$\frac{9n^2}{17m^5}$    So the exponent of m = 5, your answer is the 3rd option