Solve [(frac{3^{2}+6-16}{1})^2+9(5-4)^3]+11^2-(-6+3)^2

$$[ ( \frac { 3 ^ { 2 } + 6 - 16 } { 1 } ) ^ { 2 } + 9 ( 5 - 4 ) ^ { 3 } ] + 11 ^ { 2 } - ( - 6 + 3 ) ^ { 2 }$$

Evaluate

$$122$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{9+6-16}{1}\right)^{2}+9\left(5-4\right)^{3}+11^{2}-\left(-6+3\right)^{2}$$

Add 9 and 6 to get 15.

$$\left(\frac{15-16}{1}\right)^{2}+9\left(5-4\right)^{3}+11^{2}-\left(-6+3\right)^{2}$$

Subtract 16 from 15 to get -1.

$$\left(\frac{-1}{1}\right)^{2}+9\left(5-4\right)^{3}+11^{2}-\left(-6+3\right)^{2}$$

Anything divided by one gives itself.

$$\left(-1\right)^{2}+9\left(5-4\right)^{3}+11^{2}-\left(-6+3\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$1+9\left(5-4\right)^{3}+11^{2}-\left(-6+3\right)^{2}$$

Subtract 4 from 5 to get 1.

$$1+9\times 1^{3}+11^{2}-\left(-6+3\right)^{2}$$

Calculate 1 to the power of 3 and get 1.

$$1+9\times 1+11^{2}-\left(-6+3\right)^{2}$$

Multiply 9 and 1 to get 9.

$$1+9+11^{2}-\left(-6+3\right)^{2}$$

Add 1 and 9 to get 10.

$$10+11^{2}-\left(-6+3\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$10+121-\left(-6+3\right)^{2}$$

Add 10 and 121 to get 131.

$$131-\left(-6+3\right)^{2}$$

Add -6 and 3 to get -3.

$$131-\left(-3\right)^{2}$$

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

$$131-9$$

Subtract 9 from 131 to get 122.

$$122$$

Factor

$$2\times 61$$