Solve 1^-2/2+2^-2/3+3^-2/4

$$\frac{ { 1 }^{ -2 } }{ 2 } + \frac{ { 2 }^{ -2 } }{ 3 } + \frac{ { 3 }^{ -2 } }{ 4 }$$

Evaluate

$$\frac{11}{18}\approx 0.611111111$$

Solution Steps

Calculate 1 to the power of -2 and get 1.

$$\frac{1}{2}+\frac{2^{-2}}{3}+\frac{3^{-2}}{4}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{2}+\frac{\frac{1}{4}}{3}+\frac{3^{-2}}{4}$$

Express \frac{\frac{1}{4}}{3} as a single fraction.

$$\frac{1}{2}+\frac{1}{4\times 3}+\frac{3^{-2}}{4}$$

Multiply 4 and 3 to get 12.

$$\frac{1}{2}+\frac{1}{12}+\frac{3^{-2}}{4}$$

Add \frac{1}{2} and \frac{1}{12} to get \frac{7}{12}.

$$\frac{7}{12}+\frac{3^{-2}}{4}$$

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

$$\frac{7}{12}+\frac{\frac{1}{9}}{4}$$

Express \frac{\frac{1}{9}}{4} as a single fraction.

$$\frac{7}{12}+\frac{1}{9\times 4}$$

Multiply 9 and 4 to get 36.

$$\frac{7}{12}+\frac{1}{36}$$

Add \frac{7}{12} and \frac{1}{36} to get \frac{11}{18}.

$$\frac{11}{18}$$

Factor

$$\frac{11}{2 \cdot 3 ^ {2}} = 0.6111111111111112$$