Solve frac{(-1)^{7}(-1)^{10}(-1)^{4}}{(-1)^6(-1)^2(-1)^8}=(-1)^5=-5

$$\frac { ( - 1 ) ^ { 7 } ( - 1 ) ^ { 10 } ( - 1 ) ^ { 4 } } { ( - 1 ) ^ { 6 } ( - 1 ) ^ { 2 } ( - 1 ) ^ { 8 } } = ( - 1 ) ^ { 5 } = - 5$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 10 to get 17.

$$\frac{\left(-1\right)^{17}\left(-1\right)^{4}}{\left(-1\right)^{6}\left(-1\right)^{2}\left(-1\right)^{8}}=\left(-1\right)^{5}\text{ and }\left(-1\right)^{5}=-5$$

To multiply powers of the same base, add their exponents. Add 17 and 4 to get 21.

$$\frac{\left(-1\right)^{21}}{\left(-1\right)^{6}\left(-1\right)^{2}\left(-1\right)^{8}}=\left(-1\right)^{5}\text{ and }\left(-1\right)^{5}=-5$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\left(-1\right)^{21}}{\left(-1\right)^{8}\left(-1\right)^{8}}=\left(-1\right)^{5}\text{ and }\left(-1\right)^{5}=-5$$

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$\frac{\left(-1\right)^{21}}{\left(-1\right)^{16}}=\left(-1\right)^{5}\text{ and }\left(-1\right)^{5}=-5$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 16 from 21 to get 5.

$$\left(-1\right)^{5}=\left(-1\right)^{5}\text{ and }\left(-1\right)^{5}=-5$$

As \left(-1\right)^{5} and \left(-1\right)^{5} have the same base, compare them by comparing their exponents.

$$\text{true}\text{ and }\left(-1\right)^{5}=-5$$

Calculate -1 to the power of 5 and get -1.

$$\text{true}\text{ and }-1=-5$$

Compare -1 and -5.

$$\text{true}\text{ and }\text{false}$$

The conjunction of \text{true} and \text{false} is \text{false}.

$$\text{false}$$