What is the quotient the fraction with numerator 2 m to the 9th power n to the 4th power and denominator negative 4 m to the negative 3 power n to the negative 2 power in simplest form? Assume m is not equal to 0 , n is not equal to 0
Answer
A
6 m to the 12th power n to the 6th power
B
negative the fraction with numerator m to the 27th power n to the 8th power and denominator 2
C
8 m to the 12th power n to the 6th power
D
negative the fraction with numerator m to the 12th power n to the 6th power and denominator 2
Explanation
Divide the coefficients: 2 ÷ (−4) = −1/2. When dividing powers with the same base, subtract the exponents, so m⁹ ÷ m⁻³ = m¹² and n⁴ ÷ n⁻² = n⁶. The quotient is −m¹²n⁶/2, which is choice D.
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