how do i get the answer for [(7.6341*10^-23)/(0.968)]^-1/3?

You could so it straight on the calc

$${\left({\frac{\left({\mathtt{7.634\: \!1}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{23}}}\right)}{{\mathtt{0.968}}}}\right)}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} = {\mathtt{23\,318\,780.670\: \!183\: \!264}}$$

OR YOU CAN SIMPLIFY BY HAND FIRST

 

$$\left(\frac{7.6341\times 10^{-23}}{0.968}\right)^{-1/3}\\\\
\left(\frac{7.6341}{0.968\times 10^{+23}}\right)^{-1/3}\\\\
=\left(\frac{0.968\times 10^{+23}}{7.6341}\right)^{+1/3}\\\\$$

$${\left({\frac{{\mathtt{0.968}}{\mathtt{\,\times\,}}\left({{\mathtt{10}}}^{{\mathtt{23}}}\right)}{{\mathtt{7.634\: \!1}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} = {\mathtt{23\,318\,780.670\: \!183\: \!264}}$$

If you want to know how to deal with negative indices, look here.

http://web2.0calc.com/questions/indices-especially-negative-indices

The answer is: 23318780.7117252

 

1. 10^-23= 0.00000000000000000000001

2. 7.6341 * 0.00000000000000000000001 = 0.000000000000000000000076341

3. 0.000000000000000000000076341 / 0.968 = 0.000000000000000000000078864669

4. 0.000000000000000000000078864669 ^-1/3 (or -0.3333333333333333) = 23318780.7117252