Which expression is equivalent to the fraction with numerator 3 x to the negative 6 power y to the negative 3 power and denominator 15 x squared y to the 10th power ? Assume x is not equal to 0 , y is not equal to 0
Answer
A
the fraction with numerator y to the 7th power and denominator 5 x to the 4th power
B
the fraction with numerator 5 and denominator x to the 12th power y to the 30th power
C
the fraction with numerator 1 and denominator 5 x to the 8th power y to the 13th power
D
the fraction with numerator 5 and denominator x to the 4th power y to the 7th power
Explanation
Divide the coefficients: 3/15 = 1/5. When dividing powers with the same base, subtract exponents, so x^(-6)/x^2 = x^(-8) and y^(-3)/y^10 = y^(-13). Rewrite the negative exponents in the denominator to get 1/(5x^8y^13), which is choice C.
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