Which expression is equivalent to the fraction with numerator 28 p to the 9th power q to the negative 5 power and denominator 12 p to the negative 6 power q to the 7th power ? Assume p is not equal to 0 , q is not equal to 0
Answer
A
the fraction with numerator 7 p to the 15th power and denominator 3 q to the 12th power
B
the fraction with numerator 2 q to the 12th power and denominator p to the 15th power
C
the fraction with numerator 7 p to the 15th power q to the 12th power and denominator 3
D
the fraction with numerator 2 and denominator p to the 15th power q to the 12th power
Explanation
Divide the coefficients: 28/12 = 7/3. When dividing powers with the same base, subtract the exponents, so p⁹/p⁻⁶ = p¹⁵ and q⁻⁵/q⁷ = q⁻¹² = 1/q¹². The expression is therefore 7p¹⁵/(3q¹²), which matches choice A.
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