I will do the first, you do the second.

$\displaystyle 32^{3/5} \cdot a^{-2/3} \cdot b^2 \div (216a^4b^2)^{1/3}$

The first step is to write this thing out as a single fraction:

$\displaystyle = \frac{32^{3/5} \cdot a^{-2/3} \cdot b^2}{(216a^4b^2)^{1/3}}$

The next step is to work out the parenthesis. There is only one set of parenthesis, in the denominator:

$\displaystyle = \frac{32^{3/5} \cdot a^{-2/3} \cdot b^2}{216^{1/3} \cdot a^{4/3} \cdot b^{2/3}}$

Now write the denominator as negative powers of the numerator:

$\displaystyle = 32^{3/5} \cdot a^{-2/3} \cdot b^2 \cdot 216^{-1/3} \cdot a^{-4/3} \cdot b^{-2/3}$

Now combine powers of like bases:

$\displaystyle = 32^{3/5} \cdot 216^{-1/3} \cdot a^{-2/3 - 4/3} \cdot b^{2 - 2/3}$

$\displaystyle = 32^{3/5} \cdot 216^{-1/3} \cdot a^{-2} \cdot b^{4/3}$

Now go to work on the constants. You are expected to know (or somehow figure out) that $\displaystyle 2^5 = 32$ and $\displaystyle 6^3 = 216$:

$\displaystyle = (2^5)^{3/5} \cdot (6^3)^{-1/3} \cdot a^{-2} \cdot b^{4/3}$

$\displaystyle = 2^3 \cdot 6^{-1} \cdot a^{-2} \cdot b^{4/3}$

$\displaystyle = 8 \cdot 6^{-1} \cdot a^{-2} \cdot b^{4/3}$

Now put negative exponents in a denominator:

$\displaystyle = \frac{8b^{4/3}}{6a^2}$

And simplify:

$\displaystyle = \frac{4b^{4/3}}{3a^2}$

You do the second one and post your solution. We'll check it.

-Dan