Which expression is equivalent to 4th root of the fraction with numerator 16 x to the 11th power y to the 8th power and denominator 81 x to the 7th power y to the 6th power ? Assume x is greater than 0 and y is not equal to 0
Answer
A
the fraction with numerator 4 x open paren 4th root of y squared close paren and denominator 9
B
the fraction with numerator 2 x squared y and denominator 3
C
the fraction with numerator 2 x open paren 4th root of y squared close paren and denominator 3
D
the fraction with numerator 4 x squared y and denominator 9
Explanation
First simplify inside the fourth root: 16/81 · x^(11−7) · y^(8−6) = (16/81)x^4y^2. Taking the fourth root gives (2/3)x·⁴√(y²), since x is positive. This matches the expression with numerator 2x times the fourth root of y squared and denominator 3.
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