Factor, using the given factor. Assume all variables represent positive real numbers.
-$$( 4 m + 1 ) ^ { - 6 / 5 } + ( 4 m + 1 ) ^ { 1 / 5 } + ( 4 m + 1 ) ^ { 7 / 5 } ; \quad ( 4 m + 1 ) ^ { - 6 / 5 }$$
A) $( 4 \mathrm {~m} + 1 ) ^ { - 6 / 5 } \left[ 1 + ( 4 \mathrm {~m} + 1 ) ^ { 7 / 5 } + ( 4 \mathrm {~m} + 1 ) ^ { 13 / 5 } \right]$

B) $( 4 m + 1 ) ^ { - 6 / 5 } \left[ 1 + ( 4 m + 1 ) ^ { - 7 / 5 } + ( 4 m + 1 ) ^ { - 13 / 5 } \right]$

C) $( 4 \mathrm {~m} + 1 ) ^ { - 6 / 5 } \left[ 1 + ( 4 \mathrm {~m} + 1 ) ^ { 7 / 5 } - ( 4 \mathrm {~m} + 1 ) ^ { 13 / 5 } \right]$

D) $(4 m+1)^{-6 / 5}\left[1+(4 m+1)^{8 / 5}+(4 m+1)^{11 / 5}\right]$

Question

Factor, using the given factor. Assume all variables represent positive real numbers.
-$$( 4 m + 1 ) ^ { - 6 / 5 } + ( 4 m + 1 ) ^ { 1 / 5 } + ( 4 m + 1 ) ^ { 7 / 5 } ; \quad ( 4 m + 1 ) ^ { - 6 / 5 }$$
A) $( 4 \mathrm {~m} + 1 ) ^ { - 6 / 5 } \left[ 1 + ( 4 \mathrm {~m} + 1 ) ^ { 7 / 5 } + ( 4 \mathrm {~m} + 1 ) ^ { 13 / 5 } \right]$

B) $( 4 m + 1 ) ^ { - 6 / 5 } \left[ 1 + ( 4 m + 1 ) ^ { - 7 / 5 } + ( 4 m + 1 ) ^ { - 13 / 5 } \right]$

C) $( 4 \mathrm {~m} + 1 ) ^ { - 6 / 5 } \left[ 1 + ( 4 \mathrm {~m} + 1 ) ^ { 7 / 5 } - ( 4 \mathrm {~m} + 1 ) ^ { 13 / 5 } \right]$

D) $(4 m+1)^{-6 / 5}\left[1+(4 m+1)^{8 / 5}+(4 m+1)^{11 / 5}\right]$

Quizplus · Accepted Answer

Factoring out $(4m+1)^{-6/5}$ from each term, the exponents of the remaining terms in the brackets are adjusted by adding $6/5$ to each original exponent, resulting in exponents of $0$, $7/5$, and $13/5$.

Factor, Using the Given Factor (4m+1)−6/5+(4m+1)1/5+(4m+1)7/5;(4m+1)−6/5( 4 m + 1 ) ^ { - 6 / 5 } + ( 4 m + 1 ) ^ { 1 / 5 } + ( 4 m + 1 ) ^ { 7 / 5 } ; \quad ( 4 m + 1 ) ^ { - 6 / 5 }(4m+1)−6/5+(4m+1)1/5+(4m+1)7/5;(4m+1)−6/5

Factor, Using the Given Factor $( 4 m + 1 ) ^ { - 6 / 5 } + ( 4 m + 1 ) ^ { 1 / 5 } + ( 4 m + 1 ) ^ { 7 / 5 } ; \quad ( 4 m + 1 ) ^ { - 6 / 5 }$