Solve {5^{3}*3^{2}-2^{3}*[(6^{2}+6^{2}*15):2^{3}+3^2*17-6*(2^2*14-12^2:3^2*2)]}:53

$$\{ 5 ^ { 3 } \cdot 3 ^ { 2 } - 2 ^ { 3 } \cdot [ ( 6 ^ { 2 } + 6 ^ { 2 } \cdot 15 ) : 2 ^ { 3 } + 3 ^ { 2 } \cdot 17 - 6 \cdot ( 2 ^ { 2 } \cdot 14 - 12 ^ { 2 } : 3 ^ { 2 } \cdot 2 ) ] \} : 53$$

Evaluate

$$9$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$\frac{125\times 3^{2}-2^{3}\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{125\times 9-2^{3}\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiply 125 and 9 to get 1125.

$$\frac{1125-2^{3}\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1125-8\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1125-8\left(\frac{36+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1125-8\left(\frac{36+36\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiply 36 and 15 to get 540.

$$\frac{1125-8\left(\frac{36+540}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Add 36 and 540 to get 576.

$$\frac{1125-8\left(\frac{576}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1125-8\left(\frac{576}{8}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Divide 576 by 8 to get 72.

$$\frac{1125-8\left(72+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1125-8\left(72+9\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiply 9 and 17 to get 153.

$$\frac{1125-8\left(72+153-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Add 72 and 153 to get 225.

$$\frac{1125-8\left(225-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1125-8\left(225-6\left(4\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiply 4 and 14 to get 56.

$$\frac{1125-8\left(225-6\left(56-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{1125-8\left(225-6\left(56-\frac{144}{3^{2}}\times 2\right)\right)}{53}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1125-8\left(225-6\left(56-\frac{144}{9}\times 2\right)\right)}{53}$$

Divide 144 by 9 to get 16.

$$\frac{1125-8\left(225-6\left(56-16\times 2\right)\right)}{53}$$

Multiply 16 and 2 to get 32.

$$\frac{1125-8\left(225-6\left(56-32\right)\right)}{53}$$

Subtract 32 from 56 to get 24.

$$\frac{1125-8\left(225-6\times 24\right)}{53}$$

Multiply 6 and 24 to get 144.

$$\frac{1125-8\left(225-144\right)}{53}$$

Subtract 144 from 225 to get 81.

$$\frac{1125-8\times 81}{53}$$

Multiply 8 and 81 to get 648.

$$\frac{1125-648}{53}$$

Subtract 648 from 1125 to get 477.

$$\frac{477}{53}$$

Divide 477 by 53 to get 9.

$$9$$

Factor

$$3^{2}$$