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

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

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

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

Calculate 2 to the power of 4 and get 16.

$$\frac{16-3\left(2^{2}\times 6-3\times 2^{2}-\left(\frac{3^{2}\times 2}{2}+1\right)\right)}{3^{2}-6}$$

Calculate 2 to the power of 2 and get 4.

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

Multiply 4 and 6 to get 24.

$$\frac{16-3\left(24-3\times 2^{2}-\left(\frac{3^{2}\times 2}{2}+1\right)\right)}{3^{2}-6}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16-3\left(24-3\times 4-\left(\frac{3^{2}\times 2}{2}+1\right)\right)}{3^{2}-6}$$

Multiply 3 and 4 to get 12.

$$\frac{16-3\left(24-12-\left(\frac{3^{2}\times 2}{2}+1\right)\right)}{3^{2}-6}$$

Subtract 12 from 24 to get 12.

$$\frac{16-3\left(12-\left(\frac{3^{2}\times 2}{2}+1\right)\right)}{3^{2}-6}$$

Cancel out 2 and 2.

$$\frac{16-3\left(12-\left(3^{2}+1\right)\right)}{3^{2}-6}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16-3\left(12-\left(9+1\right)\right)}{3^{2}-6}$$

Add 9 and 1 to get 10.

$$\frac{16-3\left(12-10\right)}{3^{2}-6}$$

Subtract 10 from 12 to get 2.

$$\frac{16-3\times 2}{3^{2}-6}$$

Multiply 3 and 2 to get 6.

$$\frac{16-6}{3^{2}-6}$$

Subtract 6 from 16 to get 10.

$$\frac{10}{3^{2}-6}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{10}{9-6}$$

Subtract 6 from 9 to get 3.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$