How can you express this w/o zero or negative exponents?

[haengbon]

Homework Statement

9 - 9y^-2
____________
y^-1 - y⁰

this whole thing is then raised to 2 (I can't seem to format it that way:( )

Homework Equations

none

The Attempt at a Solution

I'm hoping someone would guide me through this :(

 

[Pengwuino]

Well, anything raised to the 0-th power is 1 so that simplifies that. I'm not entirely sure about your general question however. Are you looking for something that is simply expressed as positive exponents?

 

[haengbon]

Well, anything raised to the 0-th power is 1 so that simplifies that. I'm not entirely sure about your general question however. Are you looking for something that is simply expressed as positive exponents?

yes xD !

 

[Pengwuino]

Well you can't get away from the fact that you'll have negative exponents. You can express the entire thing as a fraction of positive exponents however if that's what you're looking for; that is, you can get to $$\frac{something}{y^2}$$.

 

[HallsofIvy]

Homework Statement

9 - 9y^-2
____________
y^-1 - y⁰

$$\left(\frac{9- 9y^{-2}}{y^{-1}- y^{0}}\right)^2$$
$$\left(9\frac{1- \frac{1}{y^2}}{\frac{1}{y}- 1}\right)^2$$

Multiply both numerator and denominator by $y^2$.

this whole thing is then raised to 2 (I can't seem to format it that way:( )

Homework Equations

none

The Attempt at a Solution

I'm hoping someone would guide me through this :(

 

[haengbon]

$$\left(\frac{9- 9y^{-2}}{y^{-1}- y^{0}}\right)^2$$
$$\left(9\frac{1- \frac{1}{y^2}}{\frac{1}{y}- 1}\right)^2$$

Multiply both numerator and denominator by $y^2$.

I can't seem to understand why both the numerator and denominator needs to be multiplied by y² :(

 

[Mark44]

Because if you multiply only the numerator but not the denominator (or vice versa) by y², you'll get something with a different value. If you multiply both numerator and denominator by the same value, you are multiplying by 1, which is the only number you can multiply by that doesn't change the value of the expression it multiplies.