Having some trouble with exponents

charlie_says

Bit stuck on this question can anyone give me a hint to what I am doing wrong? Thanks.

Part (d) the given awnser is x^(-13/12)y^(-7/2) in the book



OK my first steps are to expand all the exponents

On the top line I get

x^(-1/3), y^(3/2) and x^-1

bottom line I get

x^(-1/4)y^2

Moving back to the top line I do the division first and get

1/(x^(1/3)(y^(3/2)))

then I multiply it by x^-1 to get

1/(x^(4/3)(y^(3/2))) this is the top line for the division

So I do the division and multiply the inverse of the bottom line

1/(x^(4/3)(y^(3/2))) * (x^(-1/4)y^2)^-1

but this is where I get stuck, I can't seem to get the given awnser in any way from this point on.

Have I made an error above? I am not certain I am doing the correct step with the last inverse part?

Thanks.

Fremen

You haven't made any mistakes. I reckon it's the top line/bottom line that's throwing you off.

Start by bringing everything up to the top line so that it reads

x^(-1/3) * y^(-3/2) * x^(-1) * x^(1/4) * y^(-2) (divided by one)

and you should be fine.

ZorbaTehZ

Multiplied out is:

[latex]\displaystyle \frac{x^{\frac{-4}{3}} \div y^{\frac{3}{2}}}{x^{\frac{-1}{4}} \times y^2}[/latex]

Easy enough to get it from there.

Fremen

I couldn't help but feel that the division symbol seemed really out of place to me when I looked at the problem earlier. It just occured to me that for maths courses beyond junior cert, it's just not used anywhere.

You can pretty much go through a university maths degree and beyond without ever using a division symbol.
It's a bit mad that it's still taught, isn't it?

charlie_says

Thanks for the hints, got it out in the end. Brain turd had blocked me.