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:

`(x^5)/(x^2) =x^((5-2))=x^3`

`(x^2)/(y^4)` (You can't combine them as they have different bases of x and y)

`(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
`(x^(-3))/(1) =(1)/(x^3)`

`(1)/(y^(-3)) =(y^3)/(1)` or
`y^3`

`(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.

`(27)/(51) *m^((1-6))*n^((3-1))`

`(9)/(17) *m^(-5)*n^2` Make all the exponents positive

`(9n^2)/(17m^5)` So the exponent of m = 5, your answer is the 3rd option