Solve (-1)^25:(-1)^15+(-1)^35-(-1)^45

$$( - 1 ) ^ { 25 } : ( - 1 ) ^ { 15 } + ( - 1 ) ^ { 35 } - ( - 1 ) ^ { 45 }$$

Evaluate

$$1$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 15 from 25 to get 10.

$$\left(-1\right)^{10}+\left(-1\right)^{35}-\left(-1\right)^{45}$$

Calculate -1 to the power of 10 and get 1.

$$1+\left(-1\right)^{35}-\left(-1\right)^{45}$$

Calculate -1 to the power of 35 and get -1.

$$1-1-\left(-1\right)^{45}$$

Subtract 1 from 1 to get 0.

$$0-\left(-1\right)^{45}$$

Calculate -1 to the power of 45 and get -1.

$$0-\left(-1\right)$$

The opposite of -1 is 1.

$$0+1$$

Add 0 and 1 to get 1.

$$1$$

Factor

$$1$$