Solve [(10^{2}-7^{2}):(10+7)+3]^{3}:2^{2}-{(8^2)^3:8^4+[13-(7^2-5*1)]}:51

$$[ ( 10 ^ { 2 } - 7 ^ { 2 } ) : ( 10 + 7 ) + 3 ] ^ { 3 } : 2 ^ { 2 } - \{ ( 8 ^ { 2 } ) ^ { 3 } : 8 ^ { 4 } + [ 13 - ( 7 ^ { 2 } - 5 \times 1 ) ] \} : 51$$

Evaluate

$$\frac{907}{17}\approx 53.352941176$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(\frac{10^{2}-7^{2}}{10+7}+3\right)^{3}}{2^{2}}-\frac{\frac{8^{6}}{8^{4}}+13-\left(7^{2}-5\times 1\right)}{51}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$\frac{\left(\frac{10^{2}-7^{2}}{10+7}+3\right)^{3}}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\left(\frac{100-7^{2}}{10+7}+3\right)^{3}}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\left(\frac{100-49}{10+7}+3\right)^{3}}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Subtract 49 from 100 to get 51.

$$\frac{\left(\frac{51}{10+7}+3\right)^{3}}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Add 10 and 7 to get 17.

$$\frac{\left(\frac{51}{17}+3\right)^{3}}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Divide 51 by 17 to get 3.

$$\frac{\left(3+3\right)^{3}}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Add 3 and 3 to get 6.

$$\frac{6^{3}}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{216}{2^{2}}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{216}{4}-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Divide 216 by 4 to get 54.

$$54-\frac{8^{2}+13-\left(7^{2}-5\times 1\right)}{51}$$

Calculate 8 to the power of 2 and get 64.

$$54-\frac{64+13-\left(7^{2}-5\times 1\right)}{51}$$

Calculate 7 to the power of 2 and get 49.

$$54-\frac{64+13-\left(49-5\times 1\right)}{51}$$

Multiply 5 and 1 to get 5.

$$54-\frac{64+13-\left(49-5\right)}{51}$$

Subtract 5 from 49 to get 44.

$$54-\frac{64+13-44}{51}$$

Subtract 44 from 13 to get -31.

$$54-\frac{64-31}{51}$$

Subtract 31 from 64 to get 33.

$$54-\frac{33}{51}$$

Reduce the fraction \frac{33}{51} to lowest terms by extracting and canceling out 3.

$$54-\frac{11}{17}$$

Subtract \frac{11}{17} from 54 to get \frac{907}{17}.

$$\frac{907}{17}$$

Factor

$$\frac{907}{17} = 53\frac{6}{17} = 53.35294117647059$$