Solve {[(2^{8}:2^{5}+6^{5}:6^{3}-3*7+4^{0}):2^{3}]^{2}-(8^{3}-20^2):4^2}*2^2+5*3+1^9

$$\{ [ ( 2 ^ { 8 } : 2 ^ { 5 } + 6 ^ { 5 } : 6 ^ { 3 } - 3 \times 7 + 4 ^ { 0 } ) : 2 ^ { 3 } ] ^ { 2 } - ( 8 ^ { 3 } - 20 ^ { 2 } ) : 4 ^ { 2 } \} \times 2 ^ { 2 } + 5 \times 3 + 1 ^ { 9 }$$

Evaluate

$$24$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 8 to get 3.

$$\left(\left(\frac{2^{3}+\frac{6^{5}}{6^{3}}-3\times 7+4^{0}}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

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

$$\left(\left(\frac{2^{3}+6^{2}-3\times 7+4^{0}}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 2 to the power of 3 and get 8.

$$\left(\left(\frac{8+6^{2}-3\times 7+4^{0}}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 6 to the power of 2 and get 36.

$$\left(\left(\frac{8+36-3\times 7+4^{0}}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Add 8 and 36 to get 44.

$$\left(\left(\frac{44-3\times 7+4^{0}}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Multiply 3 and 7 to get 21.

$$\left(\left(\frac{44-21+4^{0}}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Subtract 21 from 44 to get 23.

$$\left(\left(\frac{23+4^{0}}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 4 to the power of 0 and get 1.

$$\left(\left(\frac{23+1}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Add 23 and 1 to get 24.

$$\left(\left(\frac{24}{2^{3}}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 2 to the power of 3 and get 8.

$$\left(\left(\frac{24}{8}\right)^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Divide 24 by 8 to get 3.

$$\left(3^{2}-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 3 to the power of 2 and get 9.

$$\left(9-\frac{8^{3}-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 8 to the power of 3 and get 512.

$$\left(9-\frac{512-20^{2}}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 20 to the power of 2 and get 400.

$$\left(9-\frac{512-400}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Subtract 400 from 512 to get 112.

$$\left(9-\frac{112}{4^{2}}\right)\times 2^{2}+5\times 3+1^{9}$$

Calculate 4 to the power of 2 and get 16.

$$\left(9-\frac{112}{16}\right)\times 2^{2}+5\times 3+1^{9}$$

Divide 112 by 16 to get 7.

$$\left(9-7\right)\times 2^{2}+5\times 3+1^{9}$$

Subtract 7 from 9 to get 2.

$$2\times 2^{2}+5\times 3+1^{9}$$

Calculate 2 to the power of 2 and get 4.

$$2\times 4+5\times 3+1^{9}$$

Multiply 2 and 4 to get 8.

$$8+5\times 3+1^{9}$$

Multiply 5 and 3 to get 15.

$$8+15+1^{9}$$

Add 8 and 15 to get 23.

$$23+1^{9}$$

Calculate 1 to the power of 9 and get 1.

$$23+1$$

Add 23 and 1 to get 24.

$$24$$

Factor

$$2^{3}\times 3$$