Question

Simplify the expression:

\[\frac{ 8x ^{-4}y ^{-8} }{ -2xy ^{5} }\]

Write your answer without negative exponents.

Answer 1

I know I just asked a similar question. Right now I am not clear on how to handle it if the denominator is not the same as the numerator as demonstrated above.

Answer 2

You gotta understand your indices well, recall
\[\Large \frac{a^{m}}{a^{n}}=a^{m-n}\]

Answer 3

Okay, so how would I apply that to this question? I saw that in the lesson and tried to understand, but I really can't see how it applies here.

Answer 4

So this
\[\frac{ 8x ^{-4}y ^{-8} }{ -2xy ^{5} }\]
Is simply
\[\Large -4(x^{-4-1} )( y^{-8-5})\]

Answer 5

There's a few way but this is a snappier one

Answer 6

So \[-4 \left(x ^{3}\right)\left( y ^{3} \right)\]

Answer 7

\[-4(x^{-4-1} )( y^{-8-5}) \\ \\ =-4(x^{-5} )( y^{-13})\]
Then use
\[\Large x^{-a}=\frac{1}{x^{a}}\]
\[\Large -4(\frac{1}{x^5y^{13}})\]

Answer 8

-4-1 is -5 and -8-5 is -13

Answer 9

\[-4\left( x ^{5}y ^{13} \right)\]?

Answer 10

\[\LARGE -4(x^{-4-1} )( y^{-8-5}) \\ \\ \LARGE =-4(x^{-5} )( y^{-13})\]

Answer 11

\[\LARGE =-4(x^{-5} y^{-13})\]

Answer 12

Then use
\[\Large x^{-a}=\frac{1}{x^{a}}\]

Answer 13

You'll get
\[\Large -4(\frac{1}{x^5y^{13}})\]

Answer 14

And thats the answer?

Answer 15

Yep

Answer 16

Ah, okay... thanks!