Factor, using the given factor. Assume all variables represent positive real numbers.
-$$( 2 m + 6 ) ^ { - 6 / 5 } + ( 2 m + 6 ) ^ { 1 / 5 } + ( 2 m + 6 ) ^ { 7 / 5 } ; \quad ( 2 m + 6 ) ^ { - 6 / 5 }$$
A) $( 2 m + 6 ) ^ { - 6 / 5 } \left[ 1 + ( 2 m + 6 ) ^ { 8 / 5 } + ( 2 m + 6 ) ^ { 11 / 5 } \right]$
B) $( 2 m + 6 ) ^ { - 6 / 5 } \left[ 1 + ( 2 m + 6 ) ^ { 7 / 5 } - ( 2 m + 6 ) ^ { 13 / 5 } \right]$
C) $( 2 \mathrm {~m} + 6 ) ^ { - 6 / 5 } \left[ 1 + ( 2 \mathrm {~m} + 6 ) ^ { 7 / 5 } + ( 2 \mathrm {~m} + 6 ) ^ { 13 / 5 } \right]$
D) $( 2 \mathrm {~m} + 6 ) ^ { - 6 / 5 } \left[ 1 + ( 2 \mathrm {~m} + 6 ) ^ { - 7 / 5 } + ( 2 \mathrm {~m} + 6 ) ^ { - 13 / 5 } \right]$

Question

Quizplus · Accepted Answer

Factoring out $(2m + 6)^{-6/5}$ from each term, the exponents inside the brackets are adjusted by adding $6/5$ to each of the original exponents, resulting in exponents of $0$, $7/5$, and $13/5$, which matches option C.

Factor, Using the Given Factor (2m+6)−6/5+(2m+6)1/5+(2m+6)7/5;(2m+6)−6/5( 2 m + 6 ) ^ { - 6 / 5 } + ( 2 m + 6 ) ^ { 1 / 5 } + ( 2 m + 6 ) ^ { 7 / 5 } ; \quad ( 2 m + 6 ) ^ { - 6 / 5 }(2m+6)−6/5+(2m+6)1/5+(2m+6)7/5;(2m+6)−6/5

Factor, Using the Given Factor $( 2 m + 6 ) ^ { - 6 / 5 } + ( 2 m + 6 ) ^ { 1 / 5 } + ( 2 m + 6 ) ^ { 7 / 5 } ; \quad ( 2 m + 6 ) ^ { - 6 / 5 }$