Solve (-x)^{2}x^3(-x)^5x^6(-x)^7

$$( - x ) ^ { 2 } x ^ { 3 } ( - x ) ^ { 5 } x ^ { 6 } ( - x ) ^ { 7 }$$

Evaluate

$$x^{23}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\left(-x\right)^{7}x^{3}x^{6}\left(-x\right)^{7}$$

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$\left(-x\right)^{14}x^{3}x^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\left(-x\right)^{14}x^{9}$$

Expand \left(-x\right)^{14}.

$$\left(-1\right)^{14}x^{14}x^{9}$$

Calculate -1 to the power of 14 and get 1.

$$1x^{14}x^{9}$$

To multiply powers of the same base, add their exponents. Add 14 and 9 to get 23.

$$1x^{23}$$

For any term t, t\times 1=t and 1t=t.

$$x^{23}$$

Expand

$$x^{23}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\left(-x\right)^{7}x^{3}x^{6}\left(-x\right)^{7}$$

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$\left(-x\right)^{14}x^{3}x^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\left(-x\right)^{14}x^{9}$$

Expand \left(-x\right)^{14}.

$$\left(-1\right)^{14}x^{14}x^{9}$$

Calculate -1 to the power of 14 and get 1.

$$1x^{14}x^{9}$$

To multiply powers of the same base, add their exponents. Add 14 and 9 to get 23.

$$1x^{23}$$

For any term t, t\times 1=t and 1t=t.

$$x^{23}$$