1. ## Indices

Hey, Can anyone tell me how to simplify this expression into a single power

Sorry didn't know how to write the formular on the computer, hopefully you will understand this The smaller red numbers are meant to be subscripted. Just previewed the post and the square root symbols have turned to question marks
3?a / a^2b2?a

Thankyou ^^

2. Hello, Dan!

We aren't responding because we can't read the problem.

The smaller red numbers are meant to be subscripted.
Just previewed the post and the square root symbols have turned to question marks
3?a / a^2b2?a
I think you mean "superscripted" . . . root indices.

And is that really a $\displaystyle b$ in there?

If the problem is actually: .$\displaystyle \frac{\sqrt[3]{a}}{a^2\sqrt{a}}$ . . . we have a chance.

We have: .$\displaystyle \frac{a^{\frac{1}{3}}}{a^2\cdot a^{\frac{1}{2}}} \;=\;\frac{a^{\frac{1}{3}}}{a^{\frac{5}{2}}} \;=\;a^{(\frac{1}{3}-\frac{5}{2})} \;=\;a^{-\frac{13}{6}} \;=\;\frac{1}{a^{\frac{13}{6}}}$

3. I believe you wanted to type this...
$\displaystyle \frac{^3\sqrt{a}}{a^2b\sqrt{a}}$

Reduce every radical to power form:

$\displaystyle \frac{a^{1/3}}{a^2ba^{1/2}}$

Now, reduce this to one term, by inversing the denominator like so:

$\displaystyle a^{1/3}a^{-2}b^{-1}a^{-1/2}$

Notice how all the powers in the "bottom" went negative now that they are on the "top" with the original numerator. Combine bases by adding their exponents together, and you are done:

$\displaystyle a^{1/3 - 2 - 1/2}b^{-1}$

$\displaystyle a^{\frac{2-12-3}{6}}b^{-1}$

$\displaystyle a^{\frac{-13}{6}}b^{-1}$

This is an accepted form. You could also choose to represent negative exponents as a fraction:

$\displaystyle \frac{1}{a^{\frac{13}{6}}b}$

4. Originally Posted by Soroban

And is that really a $\displaystyle b$ in there?

Yup Thanks for the reply anyways.

Colby thanks I get it now, you explained it really well.