Which expression is equivalent to the fraction with numerator negative 9 x inverse y to the negative 9 power and denominator negative 15 x to the 5th power y to the negative 3 power ? Assume x is not equal to 0 , y is not equal to 0
Answer
A
the fraction with numerator 3 and denominator 5 x to the 5th power y cubed
B
the fraction with numerator 3 and denominator 5 x to the 6th power y to the 6th power
C
the fraction with numerator 5 and denominator 3 x to the 6th power y to the 6th power
D
the fraction with numerator 5 and denominator 3 x to the 5th power y cubed
Explanation
The negative signs cancel, and the numerical fraction simplifies from 9/15 to 3/5. When dividing powers with the same base, subtract exponents: x⁻¹ ÷ x⁵ = x⁻⁶ and y⁻⁹ ÷ y⁻³ = y⁻⁶. Rewriting the negative exponents in the denominator gives 3/(5x⁶y⁶), which is choice B.
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