Simplify the expression. Assume all variables represent positive real numbers.
-$$2 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$$
A) $2 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$
B) $- 14 \sqrt [ 3 ] { 2 }$
C) $14 \sqrt [ 3 ] { 2 }$
D) $- 2 \sqrt [ 3 ] { 2 }$

Question

Quizplus · Accepted Answer

First, simplify $\sqrt[3]{128}$. Since $128 = 2^7$, $\sqrt[3]{128} = \sqrt[3]{2^7} = 2^{\frac{7}{3}} = 2^2 \cdot 2^{\frac{1}{3}} = 4\sqrt[3]{2}$. Therefore, the expression becomes $2\sqrt[3]{2} - 4(4\sqrt[3]{2}) = 2\sqrt[3]{2} - 16\sqrt[3]{2} = -14\sqrt[3]{2}$.

Simplify the Expression 223−412832 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }232​−43128​

Simplify the Expression $2 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$