Exponential and Logarithmic Functions - Properties of Exponent

SOURCE:COMPETITION
Number of Problems: 2. : (Book)

1.

'

The ratio $frac{2^{2001}cdot3^{2003}}{6^{2002}}$ is:

$mathrm{(A) } 1/6qquad mathrm{(B) } 1/3qquad mathrm{(C) } 1/2qquad mathrm{(D) } 2/3qquad mathrm{(E) } 3/2$

'

2.

'

Suppose that $P = 2^m$ and $Q = 3^n$ . Which of the following is equal to $12^{mn}$ for every pair of integers $(m,n)$ ?

$extbf{(A)} P^2Q qquad extbf{(B)} P^nQ^m qquad extbf{(C)} P^nQ^{2m} qquad extbf{(D)} P^{2m}Q^n qquad extbf{(...$

'