Solve (3*2^{2}+2)^{2}:[3^{3}-(5*2^2+1)+2]+1^3+2^3*(2^4-5*2-1)

$$( 3 \times 2 ^ { 2 } + 2 ) ^ { 2 } : [ 3 ^ { 3 } - ( 5 \times 2 ^ { 2 } + 1 ) + 2 ] + 1 ^ { 3 } + 2 ^ { 3 } \times ( 2 ^ { 4 } - 5 \times 2 - 1 )$$

Evaluate

$$\frac{131}{2}=65.5$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(3\times 4+2\right)^{2}}{3^{3}-\left(5\times 2^{2}+1\right)+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Multiply 3 and 4 to get 12.

$$\frac{\left(12+2\right)^{2}}{3^{3}-\left(5\times 2^{2}+1\right)+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Add 12 and 2 to get 14.

$$\frac{14^{2}}{3^{3}-\left(5\times 2^{2}+1\right)+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Calculate 14 to the power of 2 and get 196.

$$\frac{196}{3^{3}-\left(5\times 2^{2}+1\right)+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Calculate 3 to the power of 3 and get 27.

$$\frac{196}{27-\left(5\times 2^{2}+1\right)+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{196}{27-\left(5\times 4+1\right)+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Multiply 5 and 4 to get 20.

$$\frac{196}{27-\left(20+1\right)+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Add 20 and 1 to get 21.

$$\frac{196}{27-21+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Subtract 21 from 27 to get 6.

$$\frac{196}{6+2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Add 6 and 2 to get 8.

$$\frac{196}{8}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Reduce the fraction \frac{196}{8} to lowest terms by extracting and canceling out 4.

$$\frac{49}{2}+1^{3}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Calculate 1 to the power of 3 and get 1.

$$\frac{49}{2}+1+2^{3}\left(2^{4}-5\times 2-1\right)$$

Add \frac{49}{2} and 1 to get \frac{51}{2}.

$$\frac{51}{2}+2^{3}\left(2^{4}-5\times 2-1\right)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{51}{2}+8\left(2^{4}-5\times 2-1\right)$$

Calculate 2 to the power of 4 and get 16.

$$\frac{51}{2}+8\left(16-5\times 2-1\right)$$

Multiply 5 and 2 to get 10.

$$\frac{51}{2}+8\left(16-10-1\right)$$

Subtract 10 from 16 to get 6.

$$\frac{51}{2}+8\left(6-1\right)$$

Subtract 1 from 6 to get 5.

$$\frac{51}{2}+8\times 5$$

Multiply 8 and 5 to get 40.

$$\frac{51}{2}+40$$

Add \frac{51}{2} and 40 to get \frac{131}{2}.

$$\frac{131}{2}$$

Factor

$$\frac{131}{2} = 65\frac{1}{2} = 65.5$$