Solve frac{(-1)^{44}*(-1)^45+(-1)^47}{(-1)^100*(-1)^101}

$$\frac { ( - 1 ) ^ { 44 } \cdot ( - 1 ) ^ { 45 } + ( - 1 ) ^ { 47 } } { ( - 1 ) ^ { 100 } \cdot ( - 1 ) ^ { 101 } }$$

Evaluate

$$2$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 44 and 45 to get 89.

$$\frac{\left(-1\right)^{89}+\left(-1\right)^{47}}{\left(-1\right)^{100}\left(-1\right)^{101}}$$

To multiply powers of the same base, add their exponents. Add 100 and 101 to get 201.

$$\frac{\left(-1\right)^{89}+\left(-1\right)^{47}}{\left(-1\right)^{201}}$$

Calculate -1 to the power of 89 and get -1.

$$\frac{-1+\left(-1\right)^{47}}{\left(-1\right)^{201}}$$

Calculate -1 to the power of 47 and get -1.

$$\frac{-1-1}{\left(-1\right)^{201}}$$

Subtract 1 from -1 to get -2.

$$\frac{-2}{\left(-1\right)^{201}}$$

Calculate -1 to the power of 201 and get -1.

$$\frac{-2}{-1}$$

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$2$$

Factor

$$2$$