Solve [3(2-5)^2-4(3/2-10/4)^3]-3(7/9)]-sqrt{49}

$$[ 3 ( 2 - 5 ) ^ { 2 } - 4 ( \frac { 3 } { 2 } - \frac { 10 } { 4 } ) ^ { 3 } ] - 3 ( \frac { 7 } { 9 } ) ] - \sqrt { 49 }$$

Evaluate

$$\frac{86}{3}\approx 28.666666667$$

Solution Steps

Subtract 5 from 2 to get -3.

$$3\left(-3\right)^{2}-4\left(\frac{3}{2}-\frac{10}{4}\right)^{3}-3\times \frac{7}{9}$$

Calculate -3 to the power of 2 and get 9.

$$3\times 9-4\left(\frac{3}{2}-\frac{10}{4}\right)^{3}-3\times \frac{7}{9}$$

Multiply 3 and 9 to get 27.

$$27-4\left(\frac{3}{2}-\frac{10}{4}\right)^{3}-3\times \frac{7}{9}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$27-4\left(\frac{3}{2}-\frac{5}{2}\right)^{3}-3\times \frac{7}{9}$$

Subtract \frac{5}{2} from \frac{3}{2} to get -1.

$$27-4\left(-1\right)^{3}-3\times \frac{7}{9}$$

Calculate -1 to the power of 3 and get -1.

$$27-4\left(-1\right)-3\times \frac{7}{9}$$

Multiply 4 and -1 to get -4.

$$27-\left(-4\right)-3\times \frac{7}{9}$$

The opposite of -4 is 4.

$$27+4-3\times \frac{7}{9}$$

Add 27 and 4 to get 31.

$$31-3\times \frac{7}{9}$$

Multiply 3 and \frac{7}{9} to get \frac{7}{3}.

$$31-\frac{7}{3}$$

Subtract \frac{7}{3} from 31 to get \frac{86}{3}.

$$\frac{86}{3}$$

Factor

$$\frac{2 \cdot 43}{3} = 28\frac{2}{3} = 28.666666666666668$$