The expression equals
where , the exponent of , is:
and , the exponent of , is:
and finally , the exponent of , is:

The expression equals
where r, the exponent of g, is:
and s, the exponent of y, is:
and k, the leading coefficient is:

The expression
equals
where r, the exponent of h, is:
and t, the exponent of s, is:
and k, the leading coefficient is:

The expression equals
where , the leading coefficient, is:
and , the exponent of , is:
and , the exponent of , is:
and finally , the exponent of , is:

hopefully after understanding these questions ill be able to do the others...

2. Originally Posted by wannous
The expression equals
where , the exponent of , is:
and , the exponent of , is:
and finally , the exponent of , is:

The expression equals
where r, the exponent of g, is:
and s, the exponent of y, is:
and k, the leading coefficient is:

The expression
equals
where r, the exponent of h, is:
and t, the exponent of s, is:
and k, the leading coefficient is:

The expression equals
where , the leading coefficient, is:
and , the exponent of , is:
and , the exponent of , is:
and finally , the exponent of , is:

hopefully after understanding these questions ill be able to do the others...
this isn't calculus, it's just knowing the exponent laws of algebra.

perhaps you need a review?

Exponents: Basic Rules

3. $(\frac{x^{-3}y^4z^4}{(xy)^{-6}z^6})^{-3} = (\frac{x^{-3}y^4z^4}{x^{-6}y^{-6}z^6})^{-3} = (x^{-3-(-6)}y^{4-(-6)}z^{4-6})^{-3}$

$= (x^3y^{10}z^{-2})^{-3} = x^{3-3}y^{10-3}z^{-3-3} = y^7z^{-6} = \frac{y^7}{z^6} \Rightarrow r = 0; s=7;t=-6$

For the second, you should note that the expression inside the root is the same; Let $u=729g^2y^2$ , then: $(729y^2g^2)^{\frac{1}{3}} (729y^2g^2)^{\frac{1}{2}} = u^{\frac{1}{3}}*u^{\frac{1}{2}}$

Can you continue from here?

E: Oops, didn't see skeeter's post. Anyway, this is indeed just exponentiation rules.