CPM Homework Help : PC Problem 3-41

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3-41.

Using the laws of exponents, solve for $A$ in each of the following equations.

$5 \cdot 3 ^ { ( x + 2 ) } = A \cdot 3 ^ { x }$
Step 1(a):
$\left(5\right)3^{x}·3^{2} = \left(A\right)3^{x}$
Step 2(a):
$\left(5\right)3^{2} = \left(A\right)$
Step 3(a):
$45 = A$

$\frac { 1 } { 25 } \cdot 5 ^ { ( x + 4 ) } = A \cdot 5 ^ { x }$
Hint (b):
Follow the same thinking process as in (a).

$16 \cdot 2 ^ { ( x + 4 ) } = A \cdot 2 ^ { x }$
Hint (c):
Follow the same thinking process as in (a).

$\frac { 1 } { 3 } \cdot 3 ^ { ( x - 2 ) } = A \cdot 3 ^ { x }$
Hint (d):
Follow the same thinking process as in (a).

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