## anonymous one year ago Will fan and medal! Help please! Simplify. Express with positive exponents. Rationalize denominators. (a^(-4))/(a^(-2))

1. Owlcoffee

There's an interesting property of exponential expressions that allows us to express any negative exponent as a positive. That is: doing the reciprocate, or more visually: $A ^{-b}=\frac{ 1 }{ A^b }$

2. anonymous

okay so it could just be (a^4)/(a^2)? @Owlcoffee

3. Owlcoffee

That's not correct, if we apply it: $\frac{ a ^{-4} }{ a ^{-2} }$ Will turn into: $\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }$ So all you have to do is simplify that.

4. anonymous

I really dont know how to simplify that @owlcoffee

5. Owlcoffee

When you deal with fractions inside a fraction you have to flip one and it turns into a multiplication: $\frac{ \frac{ a }{ b } }{ \frac{ x }{ y } }=(\frac{ a }{ b })(\frac{ y }{ x })$

6. Owlcoffee

Can you move on from here?

7. anonymous

okay well (A^-4)/(b^-2) *(a^4)/(b^2)??

8. Owlcoffee

Not quite.

9. anonymous

COuld you tell me what i did wrong?

10. Owlcoffee

Yes, when we make them into: $\frac{ a ^{-4} }{ a ^{-2} }=\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }$ We already got rid of the negative expressions, so we will only focus n the right side of the expression I wrote you above, more clearly: $\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }$ And we can simplify it using the property I stated to you earlier: $\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }=(\frac{ 1 }{ a^4 })(\frac{ a^2 }{ 1 })$

11. anonymous

1/a^2?

12. Owlcoffee

Correct, nice effort.!

13. anonymous

thank you! @Owlcoffee

14. Owlcoffee

No problem, thats why I am here.