Which expression is equivalent to the fraction with numerator open paren 6 x to the 5th power z close paren cubed and denominator 4 x to the 4th power z squared ?
Answer
A
the fraction with numerator 9 x to the 11th power z to the th power and denominator 2
B
54 x to the 19th power z to the 5th power
C
54 x to the 11th power z
D
the fraction with numerator 3 x to the 4th power z squared and denominator 2
Explanation
First cube each factor in the numerator: (6x⁵z)³ = 216x¹⁵z³. Then divide by 4x⁴z²: 216 ÷ 4 = 54, x¹⁵ ÷ x⁴ = x¹¹, and z³ ÷ z² = z. The result is 54x¹¹z, choice C.
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