Which expression is equivalent to the fraction with numerator open paren 3 m to the negative 2 power n close paren to the negative 3 power and denominator 6 m n to the negative 2 power ? Assume m is not equal to 0 , n is not equal to 0
Answer
A
the fraction with numerator 4 m to the 8th power and denominator 3 n cubed
B
the fraction with numerator 8 m to the 9th power and denominator n to the 9th power
C
the fraction with numerator m to the 5th power and denominator 162 n
D
the fraction with numerator 1 and denominator 2 m cubed n
Explanation
Apply the power of −3 to each factor in the numerator: (3m⁻²n)⁻³ = 3⁻³m⁶n⁻³ = m⁶/(27n³). Dividing by 6mn⁻² is the same as multiplying by n²/(6m), so the expression becomes (m⁶/(27n³))(n²/(6m)) = m⁵/(162n). This matches the choice with numerator m to the 5th power and denominator 162n.
AI-written and checked against the verified answer.