(3/7)∛(-343)-(1/4)∛(16)+(1/2)∛(54)

Question

jim_thompson5910 · Answer

$$\large \frac{3}{7}\sqrt[3]{-343}-\frac{1}{4}\sqrt[3]{16}+\frac{1}{2}\sqrt[3]{54}$$



$$\large \frac{3}{7}\sqrt[3]{(-7)^3}-\frac{1}{4}\sqrt[3]{2^3*2}+\frac{1}{2}\sqrt[3]{3^3*2}$$



$$\large \frac{3}{7}\sqrt[3]{(-7)^3}-\frac{1}{4}\sqrt[3]{2^3}*\sqrt[3]{2}+\frac{1}{2}\sqrt[3]{3^3}*\sqrt[3]{2}$$



$$\large \frac{3}{7}(-7)-\frac{1}{4}(2)*\sqrt[3]{2}+\frac{1}{2}(3)*\sqrt[3]{2}$$



$$\large -3-\frac{1}{2}\sqrt[3]{2}+\frac{3}{2}\sqrt[3]{2}$$



$$\large -3+\sqrt[3]{2}$$



So $$\large \frac{3}{7}\sqrt[3]{-343}-\frac{1}{4}\sqrt[3]{16}+\frac{1}{2}\sqrt[3]{54}=-3+\sqrt[3]{2}$$