Solve 7/9+{left(2/3right)}^3-sqrt{1/81}

$$\frac{ 7 }{ 9 } + { \left( \frac{ 2 }{ 3 } \right) }^{ 3 } - \sqrt{ \frac{ 1 }{ 81 } }$$

Evaluate

$$\frac{26}{27}\approx 0.962962963$$

Solution Steps

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{7}{9}+\frac{8}{27}-\sqrt{\frac{1}{81}}$$

Least common multiple of 9 and 27 is 27. Convert \frac{7}{9} and \frac{8}{27} to fractions with denominator 27.

$$\frac{21}{27}+\frac{8}{27}-\sqrt{\frac{1}{81}}$$

Since \frac{21}{27} and \frac{8}{27} have the same denominator, add them by adding their numerators.

$$\frac{21+8}{27}-\sqrt{\frac{1}{81}}$$

Add 21 and 8 to get 29.

$$\frac{29}{27}-\sqrt{\frac{1}{81}}$$

Rewrite the square root of the division \frac{1}{81} as the division of square roots \frac{\sqrt{1}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{29}{27}-\frac{1}{9}$$

Least common multiple of 27 and 9 is 27. Convert \frac{29}{27} and \frac{1}{9} to fractions with denominator 27.

$$\frac{29}{27}-\frac{3}{27}$$

Since \frac{29}{27} and \frac{3}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29-3}{27}$$

Subtract 3 from 29 to get 26.

$$\frac{26}{27}$$

Factor

$$\frac{2 \cdot 13}{3 ^ {3}} = 0.9629629629629629$$