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Re: If a = (27)(3^–2^ ) and x = (6)(3 ^–1^ ), then which of the [#permalink]
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This is a tricky question, but much then again.
The main thing which this question tests if do you know the "negative powers" rule
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Negative powers/exponents:
https://www.mathsisfun.com/algebra/nega ... nents.html
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Re: If a = (27)(3^–2^ ) and x = (6)(3 ^–1^ ), then which of the [#permalink]
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Carcass wrote:

The last collection of questions for the GRE Quant - 2019



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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Re: If a = (27)(3^–2^ ) and x = (6)(3 ^–1^ ), then which of the [#permalink]
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