Carcass wrote:
If a = \((27)(3^{-2} )\) and x = \((6)(3^{-1} )\), then which of the following is equivalent to \((12)(3^{-x} ) * (15)(2^{-a} )\) ?
A) \(5(-2245)(320)\)
B) \(\frac{2}{5}\)
C) \(\frac{5}{2}\)
D) \(5(24)(38)\)
E) \(5(2245)(320)\)
GIVEN: \(a = (27)(3^{-2})\)
Rewrite as: \(a = (3^3)(3^{-2})\)
Apply Product rule to get: \(a = 3^{3 + (-2)} = 3^1 = 3\)
GIVEN: \(x = (6)(3^{-1} )\)
Rewrite as: \(a = (6)(\frac{1}{3^1}) = \frac{6}{3} = 2\)
So, \(a=3\) and \(x=2\)Now take: \((12)(3^{-x} ) * (15)(2^{-a} )\)
Replace a and x to get: \((12)(3^{-2} ) * (15)(2^{-3} )\)
Evaluate each part to get: \((12)(\frac{1}{3^2}) * (15)(\frac{1}{2^3})\)
Simplify: \((12)(\frac{1}{9}) * (15)(\frac{1}{8})\)
Simplify: \((\frac{12}{9})(\frac{15}{8})\)
Evaluate: \(\frac{180}{72}\)
Simplify: \(\frac{5}{2}\)
Answer: C
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Brent Hanneson - founder of Greenlight Test Prep