Solve [3^{4}-6*(396:3^{2}-14):5+(16*3^{3}+375:5^3):29+2^4*7]:2^2-5*2^3

$$[ 3 ^ { 4 } - 6 \cdot ( 396 : 3 ^ { 2 } - 14 ) : 5 + ( 16 \cdot 3 ^ { 3 } + 375 : 5 ^ { 3 } ) : 29 + 2 ^ { 4 } \cdot 7 ] : 2 ^ { 2 } - 5 \cdot 2 ^ { 3 }$$

Evaluate

$$3$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$\frac{81-\frac{6\left(\frac{396}{3^{2}}-14\right)}{5}+\frac{16\times 3^{3}+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{81-\frac{6\left(\frac{396}{9}-14\right)}{5}+\frac{16\times 3^{3}+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Divide 396 by 9 to get 44.

$$\frac{81-\frac{6\left(44-14\right)}{5}+\frac{16\times 3^{3}+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Subtract 14 from 44 to get 30.

$$\frac{81-\frac{6\times 30}{5}+\frac{16\times 3^{3}+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Multiply 6 and 30 to get 180.

$$\frac{81-\frac{180}{5}+\frac{16\times 3^{3}+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Divide 180 by 5 to get 36.

$$\frac{81-36+\frac{16\times 3^{3}+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Subtract 36 from 81 to get 45.

$$\frac{45+\frac{16\times 3^{3}+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{45+\frac{16\times 27+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Multiply 16 and 27 to get 432.

$$\frac{45+\frac{432+\frac{375}{5^{3}}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{45+\frac{432+\frac{375}{125}}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Divide 375 by 125 to get 3.

$$\frac{45+\frac{432+3}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Add 432 and 3 to get 435.

$$\frac{45+\frac{435}{29}+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Divide 435 by 29 to get 15.

$$\frac{45+15+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Add 45 and 15 to get 60.

$$\frac{60+2^{4}\times 7}{2^{2}}-5\times 2^{3}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{60+16\times 7}{2^{2}}-5\times 2^{3}$$

Multiply 16 and 7 to get 112.

$$\frac{60+112}{2^{2}}-5\times 2^{3}$$

Add 60 and 112 to get 172.

$$\frac{172}{2^{2}}-5\times 2^{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{172}{4}-5\times 2^{3}$$

Divide 172 by 4 to get 43.

$$43-5\times 2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$43-5\times 8$$

Multiply 5 and 8 to get 40.

$$43-40$$

Subtract 40 from 43 to get 3.

$$3$$

Factor

$$3$$