Question

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

Answer 1

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:
\[A ^{-b}=\frac{ 1 }{ A^b }\]

Answer 2

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

Answer 3

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.

Answer 4

I really dont know how to simplify that @owlcoffee

Answer 5

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

Answer 6

Can you move on from here?

Answer 7

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

Answer 8

Not quite.

Answer 9

COuld you tell me what i did wrong?

Answer 10

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:
\[\frac{ \frac{ 1 }{ a^4 } }{ \frac{ 1 }{ a^2 } }=(\frac{ 1 }{ a^4 })(\frac{ a^2 }{ 1 })\]

Answer 11

1/a^2?

Answer 12

Correct, nice effort.!

Answer 13

thank you! @Owlcoffee

Answer 14

No problem, thats why I am here.