Solve frac{1,94-sqrt[3]{(-1)^5}-(50/27)^-1}{frac{sqrt{24}sqrt{2}}{15}}

$$\frac { 1,94 - \sqrt[ 3 ] { ( - 1 ) ^ { 5 } } - ( \frac { 50 } { 27 } ) ^ { - 1 } } { \frac { \sqrt { 24 } \sqrt { 2 } } { 15 } }$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

Solution Steps

Calculate -1 to the power of 5 and get -1.

$$\frac{1,94-\sqrt[3]{-1}-\left(\frac{50}{27}\right)^{-1}}{\frac{\sqrt{24}\sqrt{2}}{15}}$$

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

$$\frac{1,94-\left(-1\right)-\left(\frac{50}{27}\right)^{-1}}{\frac{\sqrt{24}\sqrt{2}}{15}}$$

The opposite of -1 is 1.

$$\frac{1,94+1-\left(\frac{50}{27}\right)^{-1}}{\frac{\sqrt{24}\sqrt{2}}{15}}$$

Add 1,94 and 1 to get 2,94.

$$\frac{2,94-\left(\frac{50}{27}\right)^{-1}}{\frac{\sqrt{24}\sqrt{2}}{15}}$$

Calculate \frac{50}{27} to the power of -1 and get \frac{27}{50}.

$$\frac{2,94-\frac{27}{50}}{\frac{\sqrt{24}\sqrt{2}}{15}}$$

Subtract \frac{27}{50} from 2,94 to get \frac{12}{5}.

$$\frac{\frac{12}{5}}{\frac{\sqrt{24}\sqrt{2}}{15}}$$

Factor 24=2\times 12. Rewrite the square root of the product \sqrt{2\times 12} as the product of square roots \sqrt{2}\sqrt{12}.

$$\frac{\frac{12}{5}}{\frac{\sqrt{2}\sqrt{12}\sqrt{2}}{15}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\frac{12}{5}}{\frac{2\sqrt{12}}{15}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{\frac{12}{5}}{\frac{2\times 2\sqrt{3}}{15}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{12}{5}}{\frac{4\sqrt{3}}{15}}$$

Divide \frac{12}{5} by \frac{4\sqrt{3}}{15} by multiplying \frac{12}{5} by the reciprocal of \frac{4\sqrt{3}}{15}.

$$\frac{12\times 15}{5\times 4\sqrt{3}}$$

Cancel out 4\times 5 in both numerator and denominator.

$$\frac{3\times 3}{\sqrt{3}}$$

Rationalize the denominator of \frac{3\times 3}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3\times 3\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3\times 3\sqrt{3}}{3}$$

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{3}}{3}$$

Divide 9\sqrt{3} by 3 to get 3\sqrt{3}.

$$3\sqrt{3}$$