Solve 2*18-{5*2+[(3^{2}*5^2-2^3*3^3):(3*7-5-7)]^2-5}

$$2 \cdot 18 - \{ 5 \cdot 2 + [ ( 3 ^ { 2 } \cdot 5 ^ { 2 } - 2 ^ { 3 } \cdot 3 ^ { 3 } ) : ( 3 \cdot 7 - 5 - 7 ) ] ^ { 2 } - 5 \}$$

Evaluate

$$30$$

Solution Steps

Multiply 2 and 18 to get 36.

$$36-\left(5\times 2+\left(\frac{3^{2}\times 5^{2}-2^{3}\times 3^{3}}{3\times 7-5-7}\right)^{2}-5\right)$$

Multiply 5 and 2 to get 10.

$$36-\left(10+\left(\frac{3^{2}\times 5^{2}-2^{3}\times 3^{3}}{3\times 7-5-7}\right)^{2}-5\right)$$

Calculate 3 to the power of 2 and get 9.

$$36-\left(10+\left(\frac{9\times 5^{2}-2^{3}\times 3^{3}}{3\times 7-5-7}\right)^{2}-5\right)$$

Calculate 5 to the power of 2 and get 25.

$$36-\left(10+\left(\frac{9\times 25-2^{3}\times 3^{3}}{3\times 7-5-7}\right)^{2}-5\right)$$

Multiply 9 and 25 to get 225.

$$36-\left(10+\left(\frac{225-2^{3}\times 3^{3}}{3\times 7-5-7}\right)^{2}-5\right)$$

Calculate 2 to the power of 3 and get 8.

$$36-\left(10+\left(\frac{225-8\times 3^{3}}{3\times 7-5-7}\right)^{2}-5\right)$$

Calculate 3 to the power of 3 and get 27.

$$36-\left(10+\left(\frac{225-8\times 27}{3\times 7-5-7}\right)^{2}-5\right)$$

Multiply 8 and 27 to get 216.

$$36-\left(10+\left(\frac{225-216}{3\times 7-5-7}\right)^{2}-5\right)$$

Subtract 216 from 225 to get 9.

$$36-\left(10+\left(\frac{9}{3\times 7-5-7}\right)^{2}-5\right)$$

Multiply 3 and 7 to get 21.

$$36-\left(10+\left(\frac{9}{21-5-7}\right)^{2}-5\right)$$

Subtract 5 from 21 to get 16.

$$36-\left(10+\left(\frac{9}{16-7}\right)^{2}-5\right)$$

Subtract 7 from 16 to get 9.

$$36-\left(10+\left(\frac{9}{9}\right)^{2}-5\right)$$

Divide 9 by 9 to get 1.

$$36-\left(10+1^{2}-5\right)$$

Calculate 1 to the power of 2 and get 1.

$$36-\left(10+1-5\right)$$

Add 10 and 1 to get 11.

$$36-\left(11-5\right)$$

Subtract 5 from 11 to get 6.

$$36-6$$

Subtract 6 from 36 to get 30.

$$30$$

Factor

$$2\times 3\times 5$$