Factor, using the given factor. Assume all variables represent positive real numbers.
-$15 s ^ { 3 / 7 } - 15 s ^ { - 5 / 7 } ; \quad s ^ { - 5 / 7 }$
A) $\mathrm { s } ^ { 1 / 3 } \left( 15 - 15 \mathrm {~s} ^ { 8 / 15 } \right)$
B) $s ^ { 3 / 7 } \left( 15 s ^ { 8 / 7 } - 158 / 15 \right)$
C) $s ^ { - 5 / 7 } \left( 15 s ^ { 8 / 7 } - 15 s \right)$
D) $s ^ { - 5 / 7 } \left( 15 s ^ { 8 / 7 } - 15 \right)$

Question

Quizplus · Accepted Answer

To factor the given expression using $s^{ - 5 / 7 }$, we take $s^{ - 5 / 7 }$ out of each term. The first term becomes $15 s^{3/7 - (-5/7)} = 15 s^{8/7}$, and the second term simply becomes $15$, since $s^{ - 5 / 7 }$ times $s^{0}$ (which is what you get when you factor out $s^{ - 5 / 7 }$ from itself) equals 1. Therefore, the factored expression is $s^{ - 5 / 7 }(15 s^{8/7} - 15)$.

Factor, Using the Given Factor 15s3/7−15s−5/7;s−5/715 s ^ { 3 / 7 } - 15 s ^ { - 5 / 7 } ; \quad s ^ { - 5 / 7 }15s3/7−15s−5/7;s−5/7

Factor, Using the Given Factor $15 s ^ { 3 / 7 } - 15 s ^ { - 5 / 7 } ; \quad s ^ { - 5 / 7 }$