Topic : Exponential and Logarithmic Functions-Properties of Exponent
from: category_eng
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

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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{(...

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1.

frac{2^{2001}cdot3^{2003}}{6^{2002}}=frac{6^{2001}cdot 3^2}{6^{2002}}=frac{9}{6}=frac{3}{2} or mathrm{ (E) }
2.

We have 12^{mn} = (2cdot 2cdot 3)^{mn} = 2^{2mn} cdot 3^{mn} = (2^m)^{2n} cdot (3^n)^m = oxed{P^{2n} Q^m}.