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

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

Evaluate

$$-6x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate -x to the power of 2 and get x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

Combine x^{6} and x^{6} to get 2x^{6}.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$2x^{6}-8x^{6}$$

Combine 2x^{6} and -8x^{6} to get -6x^{6}.

$$-6x^{6}$$

Expand

$$-6x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate -x to the power of 2 and get x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

Combine x^{6} and x^{6} to get 2x^{6}.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$2x^{6}-8x^{6}$$

Combine 2x^{6} and -8x^{6} to get -6x^{6}.

$$-6x^{6}$$