A) Express 72 as a product of its prime factors in index form. b) Hence or otherwise evaluate the values of x and y in 2^(2x) * 3^(3y) = 72.

$$72 = 2 \times 36$$ $$36 = 2 \times 18$$ $$18 = 2 \times 9$$ $$9 = 3 \times 3$$

So, $72 = 2 \times 2 \times 2 \times 3 \times 3$.

$$72 = 2^3 \times 3^2$$

The prime factorization of 72 in index form is $\boxed{2^3 \times 3^2}$.

For base 2:

$$2x = 3$$

For base 3:

$$3y = 2$$

$$y = \frac{2}{3}$$

The values are $x = \boxed{\frac{3}{2}}$ and $y = \boxed{\frac{2}{3}}$.