Solve (-2)^109:(-8)^35-9*{-2-2*[(-2)^10:(-2)^8-2]}

$$( - 2 ) ^ { 109 } : ( - 8 ) ^ { 35 } - 9 \cdot \{ - 2 - 2 \cdot [ ( - 2 ) ^ { 10 } : ( - 2 ) ^ { 8 } - 2 ] \}$$

Evaluate

$$70$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 10 to get 2.

$$\frac{\left(-2\right)^{109}}{\left(-8\right)^{35}}-9\left(-2-2\left(\left(-2\right)^{2}-2\right)\right)$$

Calculate -2 to the power of 109 and get -649037107316853453566312041152512.

$$\frac{-649037107316853453566312041152512}{\left(-8\right)^{35}}-9\left(-2-2\left(\left(-2\right)^{2}-2\right)\right)$$

Calculate -8 to the power of 35 and get -40564819207303340847894502572032.

$$\frac{-649037107316853453566312041152512}{-40564819207303340847894502572032}-9\left(-2-2\left(\left(-2\right)^{2}-2\right)\right)$$

Divide -649037107316853453566312041152512 by -40564819207303340847894502572032 to get 16.

$$16-9\left(-2-2\left(\left(-2\right)^{2}-2\right)\right)$$

Calculate -2 to the power of 2 and get 4.

$$16-9\left(-2-2\left(4-2\right)\right)$$

Subtract 2 from 4 to get 2.

$$16-9\left(-2-2\times 2\right)$$

Multiply 2 and 2 to get 4.

$$16-9\left(-2-4\right)$$

Subtract 4 from -2 to get -6.

$$16-9\left(-6\right)$$

Multiply 9 and -6 to get -54.

$$16-\left(-54\right)$$

The opposite of -54 is 54.

$$16+54$$

Add 16 and 54 to get 70.

$$70$$

Factor

$$2\times 5\times 7$$