Solve 15^{3}:5^{3}+8^{2}:8-{[3^{2}+2*(7^2-5*2^3)]+11^4:11^2}:37-13

$$15 ^ { 3 } : 5 ^ { 3 } + 8 ^ { 2 } : 8 - \{ [ 3 ^ { 2 } + 2 \times ( 7 ^ { 2 } - 5 \times 2 ^ { 3 } ) ] + 11 ^ { 4 } : 11 ^ { 2 } \} : 37 - 13$$

Evaluate

$$18$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{15^{3}}{5^{3}}+8^{1}-\frac{3^{2}+2\left(7^{2}-5\times 2^{3}\right)+\frac{11^{4}}{11^{2}}}{37}-13$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

$$\frac{15^{3}}{5^{3}}+8^{1}-\frac{3^{2}+2\left(7^{2}-5\times 2^{3}\right)+11^{2}}{37}-13$$

Calculate 15 to the power of 3 and get 3375.

$$\frac{3375}{5^{3}}+8^{1}-\frac{3^{2}+2\left(7^{2}-5\times 2^{3}\right)+11^{2}}{37}-13$$

Calculate 5 to the power of 3 and get 125.

$$\frac{3375}{125}+8^{1}-\frac{3^{2}+2\left(7^{2}-5\times 2^{3}\right)+11^{2}}{37}-13$$

Divide 3375 by 125 to get 27.

$$27+8^{1}-\frac{3^{2}+2\left(7^{2}-5\times 2^{3}\right)+11^{2}}{37}-13$$

Calculate 8 to the power of 1 and get 8.

$$27+8-\frac{3^{2}+2\left(7^{2}-5\times 2^{3}\right)+11^{2}}{37}-13$$

Add 27 and 8 to get 35.

$$35-\frac{3^{2}+2\left(7^{2}-5\times 2^{3}\right)+11^{2}}{37}-13$$

Calculate 3 to the power of 2 and get 9.

$$35-\frac{9+2\left(7^{2}-5\times 2^{3}\right)+11^{2}}{37}-13$$

Calculate 7 to the power of 2 and get 49.

$$35-\frac{9+2\left(49-5\times 2^{3}\right)+11^{2}}{37}-13$$

Calculate 2 to the power of 3 and get 8.

$$35-\frac{9+2\left(49-5\times 8\right)+11^{2}}{37}-13$$

Multiply 5 and 8 to get 40.

$$35-\frac{9+2\left(49-40\right)+11^{2}}{37}-13$$

Subtract 40 from 49 to get 9.

$$35-\frac{9+2\times 9+11^{2}}{37}-13$$

Multiply 2 and 9 to get 18.

$$35-\frac{9+18+11^{2}}{37}-13$$

Add 9 and 18 to get 27.

$$35-\frac{27+11^{2}}{37}-13$$

Calculate 11 to the power of 2 and get 121.

$$35-\frac{27+121}{37}-13$$

Add 27 and 121 to get 148.

$$35-\frac{148}{37}-13$$

Divide 148 by 37 to get 4.

$$35-4-13$$

Subtract 4 from 35 to get 31.

$$31-13$$

Subtract 13 from 31 to get 18.

$$18$$

Factor

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