Solve 5/6(1/2-1/12)^-3+sqrt[3]{1/4:(-2)}+0,6=

$$\frac { 5 } { 6 } ( \frac { 1 } { 2 } - \frac { 1 } { 12 } ) ^ { - 3 } + \sqrt[ 3 ] { \frac { 1 } { 4 } : ( - 2 ) } + 0,6 =$$

Evaluate

$$11,62$$

Solution Steps

Subtract \frac{1}{12} from \frac{1}{2} to get \frac{5}{12}.

$$\frac{5}{6}\times \left(\frac{5}{12}\right)^{-3}+\sqrt[3]{\frac{\frac{1}{4}}{-2}}+0,6$$

Calculate \frac{5}{12} to the power of -3 and get \frac{1728}{125}.

$$\frac{5}{6}\times \frac{1728}{125}+\sqrt[3]{\frac{\frac{1}{4}}{-2}}+0,6$$

Multiply \frac{5}{6} and \frac{1728}{125} to get \frac{288}{25}.

$$\frac{288}{25}+\sqrt[3]{\frac{\frac{1}{4}}{-2}}+0,6$$

Express \frac{\frac{1}{4}}{-2} as a single fraction.

$$\frac{288}{25}+\sqrt[3]{\frac{1}{4\left(-2\right)}}+0,6$$

Multiply 4 and -2 to get -8.

$$\frac{288}{25}+\sqrt[3]{\frac{1}{-8}}+0,6$$

Fraction \frac{1}{-8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$\frac{288}{25}+\sqrt[3]{-\frac{1}{8}}+0,6$$

Calculate \sqrt[3]{-\frac{1}{8}} and get -\frac{1}{2}.

$$\frac{288}{25}-\frac{1}{2}+0,6$$

Subtract \frac{1}{2} from \frac{288}{25} to get \frac{551}{50}.

$$\frac{551}{50}+0,6$$

Add \frac{551}{50} and 0,6 to get \frac{581}{50}.

$$\frac{581}{50}$$

Factor

$$\frac{7 \cdot 83}{2 \cdot 5 ^ {2}} = 11\frac{31}{50} = 11.62$$