Solve (3(left(2-5right)^2-4{left(3/2-10^3/4right)}^+3(7/9))-sqrt{49}

$$(3( { \left(2-5 \right) }^{ 2 } -4 { \left( \frac{ 3 }{ 2 } - \frac{ { 10 }^{ 3 } }{ 4 } \right) }^{ } +3( \frac{ 7 }{ 9 } ))- \sqrt{ 49 }$$

Evaluate

$$3009$$

Solution Steps

Subtract 5 from 2 to get -3.

$$3\left(\left(-3\right)^{2}-4\left(\frac{3}{2}-\frac{10^{3}}{4}\right)^{1}+3\times \frac{7}{9}\right)-\sqrt{49}$$

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

$$3\left(9-4\left(\frac{3}{2}-\frac{10^{3}}{4}\right)^{1}+3\times \frac{7}{9}\right)-\sqrt{49}$$

Calculate 10 to the power of 3 and get 1000.

$$3\left(9-4\left(\frac{3}{2}-\frac{1000}{4}\right)^{1}+3\times \frac{7}{9}\right)-\sqrt{49}$$

Divide 1000 by 4 to get 250.

$$3\left(9-4\left(\frac{3}{2}-250\right)^{1}+3\times \frac{7}{9}\right)-\sqrt{49}$$

Subtract 250 from \frac{3}{2} to get -\frac{497}{2}.

$$3\left(9-4\left(-\frac{497}{2}\right)^{1}+3\times \frac{7}{9}\right)-\sqrt{49}$$

Calculate -\frac{497}{2} to the power of 1 and get -\frac{497}{2}.

$$3\left(9-4\left(-\frac{497}{2}\right)+3\times \frac{7}{9}\right)-\sqrt{49}$$

Multiply 4 and -\frac{497}{2} to get -994.

$$3\left(9-\left(-994\right)+3\times \frac{7}{9}\right)-\sqrt{49}$$

The opposite of -994 is 994.

$$3\left(9+994+3\times \frac{7}{9}\right)-\sqrt{49}$$

Add 9 and 994 to get 1003.

$$3\left(1003+3\times \frac{7}{9}\right)-\sqrt{49}$$

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

$$3\left(1003+\frac{7}{3}\right)-\sqrt{49}$$

Add 1003 and \frac{7}{3} to get \frac{3016}{3}.

$$3\times \frac{3016}{3}-\sqrt{49}$$

Multiply 3 and \frac{3016}{3} to get 3016.

$$3016-\sqrt{49}$$

Calculate the square root of 49 and get 7.

$$3016-7$$

Subtract 7 from 3016 to get 3009.

$$3009$$

Factor

$$3\times 17\times 59$$