Solve (-x^{4})^{3}+(x^3)^4-2(-x^2)^6

$$( - x ^ { 4 } ) ^ { 3 } + ( x ^ { 3 } ) ^ { 4 } - 2 ( - x ^ { 2 } ) ^ { 6 }$$

Evaluate

$$-2x^{12}$$

Solution Steps

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

$$\left(-x^{4}\right)^{3}+x^{12}-2\left(-x^{2}\right)^{6}$$

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

$$\left(-1\right)^{3}\left(x^{4}\right)^{3}+x^{12}-2\left(-x^{2}\right)^{6}$$

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

$$\left(-1\right)^{3}x^{12}+x^{12}-2\left(-x^{2}\right)^{6}$$

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

$$-x^{12}+x^{12}-2\left(-x^{2}\right)^{6}$$

Combine -x^{12} and x^{12} to get 0.

$$0-2\left(-x^{2}\right)^{6}$$

Expand \left(-x^{2}\right)^{6}.

$$0-2\left(-1\right)^{6}\left(x^{2}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$0-2\left(-1\right)^{6}x^{12}$$

Calculate -1 to the power of 6 and get 1.

$$0-2x^{12}$$

Anything plus zero gives itself.

$$-2x^{12}$$

Expand

$$-2x^{12}$$

Solution Steps

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

$$\left(-x^{4}\right)^{3}+x^{12}-2\left(-x^{2}\right)^{6}$$

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

$$\left(-1\right)^{3}\left(x^{4}\right)^{3}+x^{12}-2\left(-x^{2}\right)^{6}$$

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

$$\left(-1\right)^{3}x^{12}+x^{12}-2\left(-x^{2}\right)^{6}$$

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

$$-x^{12}+x^{12}-2\left(-x^{2}\right)^{6}$$

Combine -x^{12} and x^{12} to get 0.

$$0-2\left(-x^{2}\right)^{6}$$

Expand \left(-x^{2}\right)^{6}.

$$0-2\left(-1\right)^{6}\left(x^{2}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$0-2\left(-1\right)^{6}x^{12}$$

Calculate -1 to the power of 6 and get 1.

$$0-2x^{12}$$

Anything plus zero gives itself.

$$-2x^{12}$$