need help with this one:
((^3(a^4 * b)^0.5)) / ((ab^3)) ) * ((^4(a^3 * b)^0.5) / ((a^3 * b)))
a, b > 0
and i also wonder how i write the equations better, more symbols and stuff like that.
Why not learn to post in symbols? You can use LaTeX tags
Forward stroke to close the tag Do you happen to mean the following?
$\displaystyle \dfrac{\sqrt[3]{a^4b}}{ab^3} \times \dfrac{\sqrt[4]{a^3b}}{a^3b}$
LaTeX will come better with practice
If so remember that the nth root is also the fractional power: $\displaystyle \sqrt[3]{a} = a^{1/3}$
You can also use the rule that says (for $\displaystyle ab \geq 0$): $\displaystyle \sqrt[a]{bc} = \sqrt[a]{b} \times \sqrt[a]{c}$
You can always double click someone's latex code to see what they typed, it's much the same method I used to learn it
Back to the question in hand:
Once you distribute the fractional power and used the laws of exponents it should reduce to $\displaystyle \dfrac{a^{4/3}b^{1/3}}{a^1b^3} \times \dfrac{a^{3/4}b^{1/4}}{a^3b} = a^{(4/3 - 1)}b^{(1/3 - 3)} \times a^{(3/4 -3)}b^{(1/4-1)}$