Solve {left(1/3right)}^2+{left(1/3right)}^-2+{left(-1/3right)}^3+3^-2

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

Evaluate

$$\frac{248}{27}\approx 9.185185185$$

Solution Steps

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

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

Calculate \frac{1}{3} to the power of -2 and get 9.

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

Add \frac{1}{9} and 9 to get \frac{82}{9}.

$$\frac{82}{9}+\left(-\frac{1}{3}\right)^{3}+3^{-2}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$\frac{82}{9}-\frac{1}{27}+3^{-2}$$

Subtract \frac{1}{27} from \frac{82}{9} to get \frac{245}{27}.

$$\frac{245}{27}+3^{-2}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{245}{27}+\frac{1}{9}$$

Add \frac{245}{27} and \frac{1}{9} to get \frac{248}{27}.

$$\frac{248}{27}$$

Factor

$$\frac{2 ^ {3} \cdot 31}{3 ^ {3}} = 9\frac{5}{27} = 9.185185185185185$$