How did they do this simplification?

1. Nov 19, 2005

benj1

Hi everyone

having a bit of trouble going through a worked example, specifically in a section where they simplify the following

1.5L^-.7K^0.7 / 0.7L^0.3K^-0.3 = 1

therefore

1.5k^0.7-(-0.3) / 0.7L^0.3-(-0.7) = 1

part in bold is one Im having trouble with.

Any help appreciated

tried using LATEX but didn't work out at all :\
Thanks

Last edited: Nov 19, 2005
2. Nov 19, 2005

VietDao29

Do you mean to simplify:
$$\frac{1.5 L ^ {-0.7} K ^ {0.6}}{0.7 L ^ {0.3} K ^ {-0.3}}$$?
So, do you know that:
$$\frac{\alpha ^ \beta}{\alpha ^ \gamma} = \alpha ^ {\beta - \gamma}$$?
And:
$$\alpha ^ {- \beta} = \alpha ^ {0 - \beta} = \frac{a ^ 0}{a ^ \beta} = \frac{1}{\alpha ^ \beta}$$
So applying that to the expression gives:
$$\frac{1.5}{0.7} \frac{L ^ {-0.7}}{L ^ {0.3}} \frac{K ^ {0.6}}{K ^ {-0.3}} = \frac{1.5}{0.7} L ^ {-0.7 - 0.3} K ^ {0.6 - (-0.3)} = \frac{1.5}{0.7} \frac{K ^ {0.9}}{L ^ {1.0}}$$.
Do you get it now?

Last edited: Nov 19, 2005
3. Nov 19, 2005

vsage

Looks like they simply grouped similar powers in the numerator and denominator. When you move an exponent to the denominator you subtract that exponents power from the power of the same base that already exists in the denominator. It will be easier to see if you break up the division into something like $$\frac{1.5L^{-0.7}}{0.7L^{0.3}}\times\frac{K^{0.7}}{K^{-0.3}}$$.

4. Nov 19, 2005

benj1

thanks heaps for the responses viet and vsage.. much appreciated

viet: the top part you have k^0.6 - it should be k^0.7

and then the indices should cancel each other out

leaving you with

1.5K / 0.7L

Im completely lost with that tex stuff

Last edited: Nov 19, 2005
5. Nov 19, 2005

VietDao29

Just remember that you do not need '\' for numbers, or words, it's just used for functions.
Click on every LaTex image to see its code. For example, click on this one:
$$\frac{1.5 K}{0.7 L}$$

6. Nov 19, 2005

benj1

thanks again..
heres another problem

240=12L^0.5(L/2)^0.5

240=12/sqrt of 2 * L

any help.. again would be appreciated

Last edited: Nov 19, 2005
7. Nov 19, 2005

hypermonkey2

$$12L^{0.5} * \frac{L^{0.5}}{2^{0.5}}$$ is an equivalent expression to your first one since

this is just properties of exponents.
therefore you can reduce your first expression to
$$12 * \sqrt{L} * \sqrt{L} * \frac{1}{\sqrt{2}}=\frac{12}{\sqrt{2}} * L$$

hope this helps!

Last edited: Nov 19, 2005
8. Nov 19, 2005

benj1

thank you hypermonkey!

i think my lack of sleep is getting the better of me or just my complete inability at maths.

still not really understanding the 12/sqrt of 2 part

sqrt to rid the equation of indices?

why has the 12 gone to the numerator of the fraction?

this is very basic and im finding it too difficult.... *sigh*

Last edited: Nov 19, 2005
9. Nov 19, 2005

hypermonkey2

dont worry about it, we all start somewhere. just as long as you dont get discouraged, youll be mathematizing in no time.
heres what you might now realize
$$12 * \frac{1}{\sqrt{2}}=\frac{12}{1} *\frac{1}{\sqrt{2}}=\frac{12}{\sqrt{2}}$$
that is the law of fraction multiplication.
it makes sense too, since
$$2 * \frac{1}{2}=2 * 0.5=1=\frac{2}{2}$$
do you agree?

10. Nov 19, 2005

benj1

help here has been overwhelming thanks.. I think im getting it, wheter its sinking in or not.. :(

the next step is proving a bit of a problem as well :uhh:

240 = (12 / sqrt of 2) * L
L = sqrt of 2 * 240 / 12

again any help.. appreciated

Last edited: Nov 19, 2005