Solve x*(-x^2)^3*(-x^3)^4

$$x \cdot ( - x ^ { 2 } ) ^ { 3 } \cdot ( - x ^ { 3 } ) ^ { 4 }$$

Evaluate

$$-x^{19}$$

Solution Steps

Expand \left(-x^{2}\right)^{3}.

$$x\left(-1\right)^{3}\left(x^{2}\right)^{3}\left(-x^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$x\left(-1\right)^{3}x^{6}\left(-x^{3}\right)^{4}$$

Calculate -1 to the power of 3 and get -1.

$$x\left(-1\right)x^{6}\left(-x^{3}\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$x^{7}\left(-1\right)\left(-x^{3}\right)^{4}$$

Expand \left(-x^{3}\right)^{4}.

$$x^{7}\left(-1\right)\left(-1\right)^{4}\left(x^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$x^{7}\left(-1\right)\left(-1\right)^{4}x^{12}$$

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

$$x^{7}\left(-1\right)\times 1x^{12}$$

Multiply -1 and 1 to get -1.

$$x^{7}\left(-1\right)x^{12}$$

To multiply powers of the same base, add their exponents. Add 7 and 12 to get 19.

$$x^{19}\left(-1\right)$$

Expand

$$-x^{19}$$

Solution Steps

Expand \left(-x^{2}\right)^{3}.

$$x\left(-1\right)^{3}\left(x^{2}\right)^{3}\left(-x^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$x\left(-1\right)^{3}x^{6}\left(-x^{3}\right)^{4}$$

Calculate -1 to the power of 3 and get -1.

$$x\left(-1\right)x^{6}\left(-x^{3}\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$x^{7}\left(-1\right)\left(-x^{3}\right)^{4}$$

Expand \left(-x^{3}\right)^{4}.

$$x^{7}\left(-1\right)\left(-1\right)^{4}\left(x^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$x^{7}\left(-1\right)\left(-1\right)^{4}x^{12}$$

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

$$x^{7}\left(-1\right)\times 1x^{12}$$

Multiply -1 and 1 to get -1.

$$x^{7}\left(-1\right)x^{12}$$

To multiply powers of the same base, add their exponents. Add 7 and 12 to get 19.

$$x^{19}\left(-1\right)$$