Negative exponents in fractions.

[Gareth56]

Continuing through the algebra book I'm studying I came across this example but cannot decide if it's correct or not.

 

Sorry but I just cannot get to grips with the proper way to present this type of equation on this forum. Hopefully it'll make sense.

 

x^2 y^3

3z^-4

 

 

= x^2y^3z^4[/u]

3

 

Sorry i can't get the 3 directly underneath = x^2y^3z^4

 

Doesn't it work out that the 3 also comes up to the numerator? Or is it only the z^-4 that comes up if so why does the 3 stay below?

[Cap'n Refsmmat]

[math]\frac{x^2y^3}{3z^{-4}} = \frac{x^2y^3z^4}{3}[/math]

 

So yes, you're right. Only the [imath]z^{-4}[/imath] moves up. Remember that [imath]3z^{-4}[/imath] is the same as [imath]3 \times z^{-4}[/imath] -- the negative exponent only applies to [imath]z[/imath], not the 3.

Edited November 5, 2008 by Cap'n Refsmmat
oops -- LaTeX trouble

[Gareth56]

Many thanks for the clarification. Both of you

[DrP]

The 3 would come up if there were brackets around the 3z. i.e. [3z]^-4 meaning the 3 and the z are to the power of -4. But the way you have it the 3 stays on the bottom. i.e. 3z^-4 means that the z only is raised to the power of -4 and the 3 is just what it is.

 

 

EDIT:

Whoops - sorry - you beat me to it.

Edited November 5, 2008 by DrP