Solve -3/4sqrt[3]{729}div-1/2sqrt[3]{243}

$$- \frac { 3 } { 4 } \sqrt[ 3 ] { 729 } \div - \frac { 1 } { 2 } \sqrt[ 3 ] { 243 }$$

Evaluate

$$\frac{81\times 3^{\frac{2}{3}}}{2}\approx 84.243394834$$

Solution Steps

Divide -\frac{3}{4}\sqrt[3]{729} by -\frac{1}{2} by multiplying -\frac{3}{4}\sqrt[3]{729} by the reciprocal of -\frac{1}{2}.

$$\frac{-\frac{3}{4}\sqrt[3]{729}\times 2}{-1}\sqrt[3]{243}$$

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

$$\frac{-\frac{3}{4}\times 9\times 2}{-1}\sqrt[3]{243}$$

Multiply -\frac{3}{4} and 9 to get -\frac{27}{4}.

$$\frac{-\frac{27}{4}\times 2}{-1}\sqrt[3]{243}$$

Multiply -\frac{27}{4} and 2 to get -\frac{27}{2}.

$$\frac{-\frac{27}{2}}{-1}\sqrt[3]{243}$$

Express \frac{-\frac{27}{2}}{-1} as a single fraction.

$$\frac{-27}{2\left(-1\right)}\sqrt[3]{243}$$

Multiply 2 and -1 to get -2.

$$\frac{-27}{-2}\sqrt[3]{243}$$

Fraction \frac{-27}{-2} can be simplified to \frac{27}{2} by removing the negative sign from both the numerator and the denominator.

$$\frac{27}{2}\sqrt[3]{243}$$