This is a tricky question, but much then again.
The main thing which this question tests if do you know the "negative powers" rule


Negative powers/exponents:
https://www.mathsisfun.com/algebra/nega ... nents.html

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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