Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive
exponents.
-$4 x ^ { - 1 / 5 } \left( 3 x ^ { 5 } - x ^ { 1 / 5 } \right)$
A) $12 x ^ { 24 / 5 } - 1$
B) $12 x ^ { 24 / 5 } - 4$
C) $12 x ^ { 24 / 5 } - x$
D) $12 x ^ { 24 / 5 } - 4 x$

Question

Quizplus · Accepted Answer

To simplify $4 x ^ { - 1 / 5 } \left( 3 x ^ { 5 } - x ^ { 1 / 5 } \right)$, distribute $4 x ^ { - 1 / 5 }$ across the parentheses. For the first term, $4 x ^ { - 1 / 5 } \cdot 3 x ^ { 5 } = 12 x ^ { 4 + 4 / 5 } = 12 x ^ { 24 / 5 }$. For the second term, $4 x ^ { - 1 / 5 } \cdot x ^ { 1 / 5 } = 4$. Therefore, the simplified expression is $12 x ^ { 24 / 5 } - 4$.

Raise to the Power or Find the Root 4x−1/5(3x5−x1/5)4 x ^ { - 1 / 5 } \left( 3 x ^ { 5 } - x ^ { 1 / 5 } \right)4x−1/5(3x5−x1/5)

Raise to the Power or Find the Root $4 x ^ { - 1 / 5 } \left( 3 x ^ { 5 } - x ^ { 1 / 5 } \right)$