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

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

Evaluate

$$204$$

Solution Steps

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

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

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

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

Calculate 8 to the power of 2 and get 64.

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

Calculate 13 to the power of 2 and get 169.

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

Calculate 7 to the power of 2 and get 49.

$$64+169-\left(49-5\times 4\right)$$

Multiply 5 and 4 to get 20.

$$64+169-\left(49-20\right)$$

Subtract 20 from 49 to get 29.

$$64+169-29$$

Subtract 29 from 169 to get 140.

$$64+140$$

Add 64 and 140 to get 204.

$$204$$

Factor

$$2^{2}\times 3\times 17$$