Solve {left(6-39/5right)}^27/15+{left(9-39/5right)}^27/15+{left(12-frac{39}{5}right)}^2frac{1}{15}

$${ \left(6- \frac{ 39 }{ 5 } \right) }^{ 2 } \frac{ 7 }{ 15 } + { \left(9- \frac{ 39 }{ 5 } \right) }^{ 2 } \frac{ 7 }{ 15 } + { \left( 12- \frac{ 39 }{ 5 } \right) }^{ 2 } \frac{ 1 }{ 15 }$$

Evaluate

$$\frac{84}{25}=3.36$$

Solution Steps

Subtract \frac{39}{5} from 6 to get -\frac{9}{5}.

$$\left(-\frac{9}{5}\right)^{2}\times \frac{7}{15}+\left(9-\frac{39}{5}\right)^{2}\times \frac{7}{15}+\left(12-\frac{39}{5}\right)^{2}\times \frac{1}{15}$$

Calculate -\frac{9}{5} to the power of 2 and get \frac{81}{25}.

$$\frac{81}{25}\times \frac{7}{15}+\left(9-\frac{39}{5}\right)^{2}\times \frac{7}{15}+\left(12-\frac{39}{5}\right)^{2}\times \frac{1}{15}$$

Multiply \frac{81}{25} and \frac{7}{15} to get \frac{189}{125}.

$$\frac{189}{125}+\left(9-\frac{39}{5}\right)^{2}\times \frac{7}{15}+\left(12-\frac{39}{5}\right)^{2}\times \frac{1}{15}$$

Subtract \frac{39}{5} from 9 to get \frac{6}{5}.

$$\frac{189}{125}+\left(\frac{6}{5}\right)^{2}\times \frac{7}{15}+\left(12-\frac{39}{5}\right)^{2}\times \frac{1}{15}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$\frac{189}{125}+\frac{36}{25}\times \frac{7}{15}+\left(12-\frac{39}{5}\right)^{2}\times \frac{1}{15}$$

Multiply \frac{36}{25} and \frac{7}{15} to get \frac{84}{125}.

$$\frac{189}{125}+\frac{84}{125}+\left(12-\frac{39}{5}\right)^{2}\times \frac{1}{15}$$

Add \frac{189}{125} and \frac{84}{125} to get \frac{273}{125}.

$$\frac{273}{125}+\left(12-\frac{39}{5}\right)^{2}\times \frac{1}{15}$$

Subtract \frac{39}{5} from 12 to get \frac{21}{5}.

$$\frac{273}{125}+\left(\frac{21}{5}\right)^{2}\times \frac{1}{15}$$

Calculate \frac{21}{5} to the power of 2 and get \frac{441}{25}.

$$\frac{273}{125}+\frac{441}{25}\times \frac{1}{15}$$

Multiply \frac{441}{25} and \frac{1}{15} to get \frac{147}{125}.

$$\frac{273}{125}+\frac{147}{125}$$

Add \frac{273}{125} and \frac{147}{125} to get \frac{84}{25}.

$$\frac{84}{25}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 7}{5 ^ {2}} = 3\frac{9}{25} = 3.36$$