Solve frac{sqrt[3]{729}-sqrt[3]{27}}{sqrt[3]{512}+sqrt[3]{343}}

$$\frac { \sqrt[ 3 ] { 729 } - \sqrt[ 3 ] { 27 } } { \sqrt[ 3 ] { 512 } + \sqrt[ 3 ] { 343 } }$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Calculate \sqrt[3]{729} and get 9.

$$\frac{9-\sqrt[3]{27}}{\sqrt[3]{512}+\sqrt[3]{343}}$$

Calculate \sqrt[3]{27} and get 3.

$$\frac{9-3}{\sqrt[3]{512}+\sqrt[3]{343}}$$

Subtract 3 from 9 to get 6.

$$\frac{6}{\sqrt[3]{512}+\sqrt[3]{343}}$$

Calculate \sqrt[3]{512} and get 8.

$$\frac{6}{8+\sqrt[3]{343}}$$

Calculate \sqrt[3]{343} and get 7.

$$\frac{6}{8+7}$$

Add 8 and 7 to get 15.

$$\frac{6}{15}$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$