Solve (-19/3+7/4)^-1*sqrt[3]{(1/125)^-1}=

$$( - \frac { 19 } { 3 } + \frac { 7 } { 4 } ) ^ { - 1 } \cdot \sqrt[ 3 ] { ( \frac { 1 } { 125 } ) ^ { - 1 } } =$$

Evaluate

$$-\frac{12}{11}\approx -1.090909091$$

Solution Steps

Add -\frac{19}{3} and \frac{7}{4} to get -\frac{55}{12}.

$$\left(-\frac{55}{12}\right)^{-1}\sqrt[3]{\left(\frac{1}{125}\right)^{-1}}$$

Calculate -\frac{55}{12} to the power of -1 and get -\frac{12}{55}.

$$-\frac{12}{55}\sqrt[3]{\left(\frac{1}{125}\right)^{-1}}$$

Calculate \frac{1}{125} to the power of -1 and get 125.

$$-\frac{12}{55}\sqrt[3]{125}$$

Calculate \sqrt[3]{125} and get 5.

$$-\frac{12}{55}\times 5$$

Multiply -\frac{12}{55} and 5 to get -\frac{12}{11}.

$$-\frac{12}{11}$$

Factor

$$-\frac{12}{11} = -1\frac{1}{11} = -1.0909090909090908$$