Which expression is equivalent to the fraction with numerator open paren A squared b to the 4th power c close paren squared times open paren 6 A cubed b close paren times open paren 2 c to the 5th power close paren cubed and denominator 4 A to the 6th power b to the 12th power c cubed ?

Apply the power rule to each grouped factor: (a²b⁴c)² = a⁴b⁸c² and (2c⁵)³ = 8c¹⁵. The numerical factor becomes (6 × 8) ÷ 4 = 12, while the variable exponents simplify to a⁴⁺³⁻⁶ = a, b⁸⁺¹⁻¹² = b⁻³, and c²⁺¹⁵⁻³ = c¹⁴. Thus the expression is 12ac¹⁴/b³, which is choice D.

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