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

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

Evaluate

$$-4$$

Solution Steps

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

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

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

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

Calculate 8 to the power of 2 and get 64.

$$\frac{-\left(64+13^{2}-\left(7^{2}-5\times 4\right)\right)}{51}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{-\left(64+169-\left(7^{2}-5\times 4\right)\right)}{51}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{-\left(64+169-\left(49-5\times 4\right)\right)}{51}$$

Multiply 5 and 4 to get 20.

$$\frac{-\left(64+169-\left(49-20\right)\right)}{51}$$

Subtract 20 from 49 to get 29.

$$\frac{-\left(64+169-29\right)}{51}$$

Subtract 29 from 169 to get 140.

$$\frac{-\left(64+140\right)}{51}$$

Add 64 and 140 to get 204.

$$\frac{-204}{51}$$

Divide -204 by 51 to get -4.

$$-4$$

Factor

$$-4$$