What value of c makes the equation true? Assume x is greater than 0 and y is greater than 0 cube root of the fraction with numerator x cubed and denominator c y to the 4th power is equal to the fraction with numerator x and denominator 4 y open paren cube root of y close paren

Because x and y are positive, the left side simplifies to x divided by (cube root of c) times y to the 4/3 power. The right side is x divided by 4 times y to the 4/3 power, since y times the cube root of y equals y to the 4/3 power. Canceling the matching factors gives cube root of c = 4, so c = 4³ = 64. The correct choice is c is equal to 64.

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