Solve sqrt{16/81}*sqrt{(-23)^2}divsqrt[3]{8*27}

$$\sqrt { \frac { 16 } { 81 } } \cdot \sqrt { ( - 23 ) ^ { 2 } } \div \sqrt[ 3 ] { 8 \cdot 27 }$$

Evaluate

$$\frac{46}{27}\approx 1.703703704$$

Solution Steps

Rewrite the square root of the division \frac{16}{81} as the division of square roots \frac{\sqrt{16}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{\frac{4}{9}\sqrt{\left(-23\right)^{2}}}{\sqrt[3]{8\times 27}}$$

Calculate -23 to the power of 2 and get 529.

$$\frac{\frac{4}{9}\sqrt{529}}{\sqrt[3]{8\times 27}}$$

Calculate the square root of 529 and get 23.

$$\frac{\frac{4}{9}\times 23}{\sqrt[3]{8\times 27}}$$

Multiply \frac{4}{9} and 23 to get \frac{92}{9}.

$$\frac{\frac{92}{9}}{\sqrt[3]{8\times 27}}$$

Multiply 8 and 27 to get 216.

$$\frac{\frac{92}{9}}{\sqrt[3]{216}}$$

Calculate \sqrt[3]{216} and get 6.

$$\frac{\frac{92}{9}}{6}$$

Express \frac{\frac{92}{9}}{6} as a single fraction.

$$\frac{92}{9\times 6}$$

Multiply 9 and 6 to get 54.

$$\frac{92}{54}$$

Reduce the fraction \frac{92}{54} to lowest terms by extracting and canceling out 2.

$$\frac{46}{27}$$

Factor

$$\frac{2 \cdot 23}{3 ^ {3}} = 1\frac{19}{27} = 1.7037037037037037$$