Factor Algebraic Expressions Containing Fractional and Negative Exponents
-$$( x + 4 ) ^ { - 1 / 3 } - ( x + 4 ) ^ { - 2 / 3 }$$

Question

Quizplus · Accepted Answer

To factor the expression, we look for a common factor in both terms. The term with the higher negative exponent $(x + 4)^{-2/3}$ can be factored out, leaving us with $(x + 4)^{-1/3} - 1$ in the numerator and $(x + 4)^{-2/3}$ as the common factor. When we adjust the exponents, we get $\frac{(x + 4)^{1/3} - 1}{(x + 4)^{2/3}}$, which matches choice A.

Factor Algebraic Expressions Containing Fractional and Negative Exponents - (x+4)−1/3−(x+4)−2/3( x + 4 ) ^ { - 1 / 3 } - ( x + 4 ) ^ { - 2 / 3 }(x+4)−1/3−(x+4)−2/3

Factor Algebraic Expressions Containing Fractional and Negative Exponents
- $( x + 4 ) ^ { - 1 / 3 } - ( x + 4 ) ^ { - 2 / 3 }$