What is the quotient the fraction with numerator 15 p to the negative 4 power q to the negative 6 power and denominator negative 20 p to the negative 12 power q to the negative 3 power in simplified form? Assume p is not equal to 0 , q is not equal to 0
Answer
A
negative the fraction with numerator p to the 8th power and denominator 5 q cubed
B
negative the fraction with numerator 3 p to the 8th power and denominator 4 q cubed
C
negative the fraction with numerator 3 and denominator 4 p to the 16th power q to the 9th power
D
negative the fraction with numerator 1 and denominator 5 p to the 16th power q to the 9th power
Explanation
Divide the coefficients: 15 ÷ (−20) = −3/4. When dividing powers with the same base, subtract the exponents: p^(−4 − (−12)) = p^8 and q^(−6 − (−3)) = q^(−3). Since q^(−3) = 1/q^3, the simplified quotient is −3p^8/(4q^3), which is choice B.
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