Solve (-2)^{3}*(-1)^1-(-2)^1*5+(-1)^3*(-1)*(-5)^4

$$( - 2 ) ^ { 3 } \cdot ( - 1 ) ^ { 1 } - ( - 2 ) ^ { 1 } \cdot 5 + ( - 1 ) ^ { 3 } \cdot ( - 1 ) \cdot ( - 5 ) ^ { 4 }$$

Evaluate

$$643$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(-2\right)^{3}\left(-1\right)^{1}-\left(-2\right)^{1}\times 5+\left(-1\right)^{4}\left(-5\right)^{4}$$

Calculate -2 to the power of 3 and get -8.

$$-8\left(-1\right)^{1}-\left(-2\right)^{1}\times 5+\left(-1\right)^{4}\left(-5\right)^{4}$$

Calculate -1 to the power of 1 and get -1.

$$-8\left(-1\right)-\left(-2\right)^{1}\times 5+\left(-1\right)^{4}\left(-5\right)^{4}$$

Multiply -8 and -1 to get 8.

$$8-\left(-2\right)^{1}\times 5+\left(-1\right)^{4}\left(-5\right)^{4}$$

Calculate -2 to the power of 1 and get -2.

$$8-\left(-2\times 5\right)+\left(-1\right)^{4}\left(-5\right)^{4}$$

Multiply -2 and 5 to get -10.

$$8-\left(-10\right)+\left(-1\right)^{4}\left(-5\right)^{4}$$

The opposite of -10 is 10.

$$8+10+\left(-1\right)^{4}\left(-5\right)^{4}$$

Add 8 and 10 to get 18.

$$18+\left(-1\right)^{4}\left(-5\right)^{4}$$

Calculate -1 to the power of 4 and get 1.

$$18+1\left(-5\right)^{4}$$

Calculate -5 to the power of 4 and get 625.

$$18+1\times 625$$

Multiply 1 and 625 to get 625.

$$18+625$$

Add 18 and 625 to get 643.

$$643$$

Factor

$$643$$