Which expression is equivalent to the fraction with numerator open paren 2 m n close paren to the 4th power and denominator 6 m to the negative 3 power 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 8 m to the 7th power n to the 6th power and denominator 3
B
the fraction with numerator 8 m to the 16th power n to the 12th power and denominator 3
C
the fraction with numerator m to the 4th power n to the 6th power and denominator 3
D
the fraction with numerator 10 m to the 7th power n to the 6th power and denominator 3
Explanation
Raise each factor in (2mn)^4 to the fourth power: the numerator becomes 16m^4n^4. Dividing by 6m^-3n^-2 is equivalent to multiplying by m^3n^2/6, so the result is (16/6)m^7n^6 = 8m^7n^6/3. This matches choice A.
AI-written and checked against the verified answer.