Solve frac{sqrt{3:(3^{3}*3^0)}-0,5+(2*3)^3/2*2^2*3^-5}{5}

$$\frac { \sqrt { 3 : ( 3 ^ { 3 } \cdot 3 ^ { 0 } ) } - 0,5 + \frac { ( 2 \cdot 3 ) ^ { 3 } } { 2 \cdot 2 ^ { 2 } \cdot 3 ^ { - 5 } } } { 5 }$$

Evaluate

$$\frac{7873}{6}\approx 1312,166666667$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$\frac{\sqrt{\frac{3}{3^{3}}}-0,5+\frac{\left(2\times 3\right)^{3}}{2\times 2^{2}\times 3^{-5}}}{5}$$

Rewrite 3^{3} as 3\times 3^{2}. Cancel out 3 in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{\sqrt{\frac{1}{9}}-0,5+\frac{\left(2\times 3\right)^{3}}{2^{3}\times 3^{-5}}}{5}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{3}-0,5+\frac{\left(2\times 3\right)^{3}}{2^{3}\times 3^{-5}}}{5}$$

Subtract 0,5 from \frac{1}{3} to get -\frac{1}{6}.

$$\frac{-\frac{1}{6}+\frac{\left(2\times 3\right)^{3}}{2^{3}\times 3^{-5}}}{5}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{1}{6}+\frac{6^{3}}{2^{3}\times 3^{-5}}}{5}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{-\frac{1}{6}+\frac{216}{2^{3}\times 3^{-5}}}{5}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-\frac{1}{6}+\frac{216}{8\times 3^{-5}}}{5}$$

Calculate 3 to the power of -5 and get \frac{1}{243}.

$$\frac{-\frac{1}{6}+\frac{216}{8\times \frac{1}{243}}}{5}$$

Multiply 8 and \frac{1}{243} to get \frac{8}{243}.

$$\frac{-\frac{1}{6}+\frac{216}{\frac{8}{243}}}{5}$$

Divide 216 by \frac{8}{243} by multiplying 216 by the reciprocal of \frac{8}{243}.

$$\frac{-\frac{1}{6}+216\times \frac{243}{8}}{5}$$

Multiply 216 and \frac{243}{8} to get 6561.

$$\frac{-\frac{1}{6}+6561}{5}$$

Add -\frac{1}{6} and 6561 to get \frac{39365}{6}.

$$\frac{\frac{39365}{6}}{5}$$

Express \frac{\frac{39365}{6}}{5} as a single fraction.

$$\frac{39365}{6\times 5}$$

Multiply 6 and 5 to get 30.

$$\frac{39365}{30}$$

Reduce the fraction \frac{39365}{30} to lowest terms by extracting and canceling out 5.

$$\frac{7873}{6}$$

Factor

$$\frac{7873}{2 \cdot 3} = 1312\frac{1}{6} = 1312.1666666666667$$