Which shows the following expression after the negative exponents have been eliminated? the fraction with numerator x y to the negative 6 power and denominator x to the negative 4 power y squared , x is not equal to 0 , y is not equal to 0
Answer
A
the fraction with numerator x to the 4th power and denominator y squared x y to the 6th power
B
the fraction with numerator x x to the 4th power and denominator y squared y to the 6th power
C
the fraction with numerator x to the 4th power y squared and denominator x y to the 6th power
D
the fraction with numerator x to the 4th power and denominator y squared x to the 6th power y to the 6th power
Explanation
Combine powers with the same base when dividing by subtracting exponents: x¹ ÷ x⁻⁴ = x⁽¹⁻⁽⁻⁴⁾⁾ = x⁵, and y⁻⁶ ÷ y² = y⁽⁻⁶⁻²⁾ = y⁻⁸. Thus the expression is x⁵y⁻⁸, which becomes x⁵/y⁸ after eliminating the negative exponent. Choice B shows this as x·x⁴ divided by y²·y⁶.
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