Solve (2^{4}+3*2^{3}):5+[2^{2}*3*5+(3*2^{2})^{2}-(2^3*3^2*5):6:3-12^2:3^2]:43

$$( 2 ^ { 4 } + 3 \cdot 2 ^ { 3 } ) : 5 + [ 2 ^ { 2 } \cdot 3 \cdot 5 + ( 3 \cdot 2 ^ { 2 } ) ^ { 2 } - ( 2 ^ { 3 } \cdot 3 ^ { 2 } \cdot 5 ) : 6 : 3 - 12 ^ { 2 } : 3 ^ { 2 } ] : 43$$

Evaluate

$$\frac{512}{43}\approx 11.906976744$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\frac{16+3\times 2^{3}}{5}+\frac{2^{2}\times 3\times 5+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{16+3\times 8}{5}+\frac{2^{2}\times 3\times 5+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Multiply 3 and 8 to get 24.

$$\frac{16+24}{5}+\frac{2^{2}\times 3\times 5+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Add 16 and 24 to get 40.

$$\frac{40}{5}+\frac{2^{2}\times 3\times 5+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Divide 40 by 5 to get 8.

$$8+\frac{2^{2}\times 3\times 5+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Calculate 2 to the power of 2 and get 4.

$$8+\frac{4\times 3\times 5+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Multiply 4 and 3 to get 12.

$$8+\frac{12\times 5+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Multiply 12 and 5 to get 60.

$$8+\frac{60+\left(3\times 2^{2}\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Calculate 2 to the power of 2 and get 4.

$$8+\frac{60+\left(3\times 4\right)^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Multiply 3 and 4 to get 12.

$$8+\frac{60+12^{2}-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Calculate 12 to the power of 2 and get 144.

$$8+\frac{60+144-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Add 60 and 144 to get 204.

$$8+\frac{204-\frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3}-\frac{12^{2}}{3^{2}}}{43}$$

Express \frac{\frac{2^{3}\times 3^{2}\times 5}{6}}{3} as a single fraction.

$$8+\frac{204-\frac{2^{3}\times 3^{2}\times 5}{6\times 3}-\frac{12^{2}}{3^{2}}}{43}$$

Cancel out 3 in both numerator and denominator.

$$8+\frac{204-\frac{3\times 5\times 2^{3}}{6}-\frac{12^{2}}{3^{2}}}{43}$$

Cancel out 3 in both numerator and denominator.

$$8+\frac{204-\frac{5\times 2^{3}}{2}-\frac{12^{2}}{3^{2}}}{43}$$

Cancel out 2 in both numerator and denominator.

$$8+\frac{204-5\times 2^{2}-\frac{12^{2}}{3^{2}}}{43}$$

Calculate 12 to the power of 2 and get 144.

$$8+\frac{204-5\times 2^{2}-\frac{144}{3^{2}}}{43}$$

Calculate 3 to the power of 2 and get 9.

$$8+\frac{204-5\times 2^{2}-\frac{144}{9}}{43}$$

Divide 144 by 9 to get 16.

$$8+\frac{204-5\times 2^{2}-16}{43}$$

Subtract 16 from 204 to get 188.

$$8+\frac{188-5\times 2^{2}}{43}$$

Calculate 2 to the power of 2 and get 4.

$$8+\frac{188-5\times 4}{43}$$

Multiply 5 and 4 to get 20.

$$8+\frac{188-20}{43}$$

Subtract 20 from 188 to get 168.

$$8+\frac{168}{43}$$

Add 8 and \frac{168}{43} to get \frac{512}{43}.

$$\frac{512}{43}$$

Factor

$$\frac{2 ^ {9}}{43} = 11\frac{39}{43} = 11.906976744186046$$