What is the quotient the fraction with numerator negative 8 A to the 8th power b to the negative 2 power and denominator 10 A to the negative 4 power b to the negative 10 power in simplified form? Assume A is not equal to 0 , b is not equal to 0
Answer
A
negative the fraction with numerator 4 A to the 12th power b to the 8th power and denominator 5
B
negative the fraction with numerator 4 A to the 32th power b to the 5th power and denominator 5
C
the fraction with numerator A to the 12th power b to the 8th power and denominator 80
D
the fraction with numerator A to the 32th power b to the 5th power and denominator 80
Explanation
Divide the coefficients: −8 ÷ 10 = −4/5. When dividing powers with the same base, subtract the exponents: A⁸ ÷ A⁻⁴ = A¹² and b⁻² ÷ b⁻¹⁰ = b⁸. So the simplified quotient is −4A¹²b⁸/5, which is choice D.
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