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

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

Evaluate

$$\frac{109}{4}=27.25$$

Solution Steps

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

$$9+\left(\frac{2}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}$$

Calculate \frac{2}{3} to the power of -2 and get \frac{9}{4}.

$$9+\frac{9}{4}+\left(\frac{1}{4}\right)^{-2}$$

Add 9 and \frac{9}{4} to get \frac{45}{4}.

$$\frac{45}{4}+\left(\frac{1}{4}\right)^{-2}$$

Calculate \frac{1}{4} to the power of -2 and get 16.

$$\frac{45}{4}+16$$

Add \frac{45}{4} and 16 to get \frac{109}{4}.

$$\frac{109}{4}$$

Factor

$$\frac{109}{2 ^ {2}} = 27\frac{1}{4} = 27.25$$