Which expression is equivalent to open paren the fraction with numerator open paren 3 x y to the negative 5 power close paren cubed and denominator open paren x to the negative 2 power y squared close paren to the negative 4 power close paren to the negative 2 power ? Assume x is not equal to 0 , y is not equal to 0
Answer
A
the fraction with numerator 18 y to the 46th power and denominator x to the 22th power
B
the fraction with numerator x to the 10th power y to the 14th power and denominator 729
C
the fraction with numerator 729 and denominator x to the 10th power y to the 14th power
D
the fraction with numerator x to the 22th power and denominator 18 y to the 46th power
Explanation
First simplify the numerator: (3xy⁻⁵)³ = 27x³y⁻¹⁵. The denominator is (x⁻²y²)⁻⁴ = x⁸y⁻⁸, so the fraction inside the outer parentheses becomes 27x⁻⁵y⁻⁷. Raising this to the power −2 gives 27⁻²x¹⁰y¹⁴ = x¹⁰y¹⁴/729, which matches the expression in choice B.
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