Simplify.
-$5 \sqrt [ 3 ] { x ^ { 2 } } \left( \sqrt [ 3 ] { 25 x } - \sqrt [ 3 ] { 25 x ^ { 8 } } \right)$
A) $25 x - 5 x ^ { 9 } \sqrt [ 3 ] { 25 }$
B) $25 x - 5 x ^ { 3 } \sqrt [ 3 ] { 5 x }$
C) $5 x \sqrt [ 3 ] { 25 } - 5 x ^ { 3 } \sqrt [ 3 ] { 25 x }$
D) $5 x \sqrt [ 3 ] { 25 x } - 5 x ^ { 3 } \sqrt [ 3 ] { 5 }$

Question

Quizplus · Accepted Answer

First, simplify inside the parentheses: $\sqrt[3]{25x} - \sqrt[3]{25x^8} = \sqrt[3]{25x} - \sqrt[3]{25}\sqrt[3]{x^8}$. Then, distribute $5\sqrt[3]{x^2}$ across the terms inside the parentheses. For the first term, $5\sqrt[3]{x^2}\sqrt[3]{25x} = 5x\sqrt[3]{25}$ because $\sqrt[3]{x^2}\sqrt[3]{x} = x$. For the second term, $5\sqrt[3]{x^2}\sqrt[3]{25}\sqrt[3]{x^8} = 5x^3\sqrt[3]{25x}$ because $\sqrt[3]{x^2}\sqrt[3]{x^8} = x^3$. Therefore, the simplified expression is $5x\sqrt[3]{25} - 5x^3\sqrt[3]{25x}$.

Simplify - 5x23(25x3−25x83)5 \sqrt [ 3 ] { x ^ { 2 } } \left( \sqrt [ 3 ] { 25 x } - \sqrt [ 3 ] { 25 x ^ { 8 } } \right)53x2​(325x​−325x8​)

Simplify
- $5 \sqrt [ 3 ] { x ^ { 2 } } \left( \sqrt [ 3 ] { 25 x } - \sqrt [ 3 ] { 25 x ^ { 8 } } \right)$