Solve {2^{1}*[5-(2-3:6^0)^2]-2*3^1}^3

$$\{ 2 ^ { 1 } \cdot [ 5 - ( 2 - 3 : 6 ^ { 0 } ) ^ { 2 } ] - 2 \cdot 3 ^ { 1 } \} ^ { 3 }$$

Evaluate

$$8$$

Solution Steps

Calculate 2 to the power of 1 and get 2.

$$\left(2\left(5-\left(2-\frac{3}{6^{0}}\right)^{2}\right)-2\times 3^{1}\right)^{3}$$

Calculate 6 to the power of 0 and get 1.

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

Anything divided by one gives itself.

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

Subtract 3 from 2 to get -1.

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

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

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

Subtract 1 from 5 to get 4.

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

Multiply 2 and 4 to get 8.

$$\left(8-2\times 3^{1}\right)^{3}$$

Calculate 3 to the power of 1 and get 3.

$$\left(8-2\times 3\right)^{3}$$

Multiply 2 and 3 to get 6.

$$\left(8-6\right)^{3}$$

Subtract 6 from 8 to get 2.

$$2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$8$$

Factor

$$2^{3}$$