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Exponential and Logarithmic Functions - Properties of Exponent

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

Problem Num : 1

Type:

Topic:Exponential and Logarithmic Functions

Adjustment# : 0

Difficulty: 1

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The ratio $frac{2^{2001}cdot3^{2003}}{6^{2002}}$ is:
$mathrm{(A) } 1/6qquad mathrm{(B) } 1/3qquad mathrm{(C) } 1/2qquad mathrm{(D) } 2/3qquad mathrm{(E) } 3/2$
'

Category Properties of Exponent

Analysis

Solution/Hint
$frac{2^{2001}cdot3^{2003}}{6^{2002}}=frac{6^{2001}cdot 3^2}{6^{2002}}=frac{9}{6}=frac{3}{2}$ or $mathrm{ (E) }$

Problem Num : 2

Type:

Topic:Exponential and Logarithmic Functions

Adjustment# : 0

Difficulty: 1

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

Category Properties of Exponent

Analysis

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