Question

Will mark brainliest!
Combine and simplify the following radical expressions:

Answer 1

Given radical expression: $6\sqrt[3]{-16}+\frac{2}{3}\sqrt[3]{-54}-5\sqrt[3]{250}$.

$6\sqrt[3]{-16} = -6\sqrt[3]{2^4} = -6\sqrt[3]{2^3\cdot \:2}=-6\cdot \:2\sqrt[3]{2} =-12\sqrt[3]{2}$

$\frac{2}{3}\sqrt[3]{-54}=\frac{2}{3}(-\sqrt[3]{3^3\cdot \:2}) =-\frac{2}{3}\cdot \:3\sqrt[3]{2} =-2\sqrt[3]{2}$

$5\sqrt[3]{250}=5\sqrt[3]{5^3\cdot \:2}=5\cdot \:5\sqrt[3]{2}=25\sqrt[3]{2}$

$6\sqrt[3]{-16}+\frac{2}{3}\sqrt[3]{-54}-5\sqrt[3]{250}=-12\sqrt[3]{2}-2\sqrt[3]{2}-25\sqrt[3]{2}$

$=-14\sqrt[3]{2}-25\sqrt[3]{2}$

$=-39\sqrt[3]{2}$