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

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

Evaluate

$$\frac{11437}{144}\approx 79.423611111$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 4 and 3 to get 12.

$$\left(9-\frac{1}{12}\right)^{2}-\left(\frac{1}{3}-\frac{1}{4}\right)$$

Subtract \frac{1}{12} from 9 to get \frac{107}{12}.

$$\left(\frac{107}{12}\right)^{2}-\left(\frac{1}{3}-\frac{1}{4}\right)$$

Calculate \frac{107}{12} to the power of 2 and get \frac{11449}{144}.

$$\frac{11449}{144}-\left(\frac{1}{3}-\frac{1}{4}\right)$$

Subtract \frac{1}{4} from \frac{1}{3} to get \frac{1}{12}.

$$\frac{11449}{144}-\frac{1}{12}$$

Subtract \frac{1}{12} from \frac{11449}{144} to get \frac{11437}{144}.

$$\frac{11437}{144}$$

Factor

$$\frac{11437}{2 ^ {4} \cdot 3 ^ {2}} = 79\frac{61}{144} = 79.42361111111111$$