Solve 2x^8divx^2+left(-2x^2right)^3-3{x}^2{x}^4

$$2 { x }^{ 8 } \div { x }^{ 2 } + { \left(-2 { x }^{ 2 } \right) }^{ 3 } -3 { x }^{ 2 } { x }^{ 4 }$$

Evaluate

$$-9x^{6}$$

Solution Steps

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

$$\frac{2x^{8}}{x^{2}}+\left(-2x^{2}\right)^{3}-3x^{6}$$

Cancel out x^{2} in both numerator and denominator.

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

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

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

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

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

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

$$2x^{6}-8x^{6}-3x^{6}$$

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

$$-6x^{6}-3x^{6}$$

Combine -6x^{6} and -3x^{6} to get -9x^{6}.

$$-9x^{6}$$

Expand

$$-9x^{6}$$

Solution Steps

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

$$\frac{2x^{8}}{x^{2}}+\left(-2x^{2}\right)^{3}-3x^{6}$$

Cancel out x^{2} in both numerator and denominator.

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

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

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

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

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

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

$$2x^{6}-8x^{6}-3x^{6}$$

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

$$-6x^{6}-3x^{6}$$

Combine -6x^{6} and -3x^{6} to get -9x^{6}.

$$-9x^{6}$$