Which expression is equivalent to cube root of the fraction with numerator 75 A to the 7th power b to the 4th power and denominator 40 A to the 13th power c to the 9th power ? Assume A is not equal to 0 and c is not equal to 0

Rewrite the fraction inside the cube root as (15b⁴)/(8A⁶c⁹), since 75/40 = 15/8 and A⁷/A¹³ = 1/A⁶. Taking the cube root gives b∛(15b)/(2A²c³), because 8, A⁶, and c⁹ are perfect cubes. This matches choice C.

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