Solve left(-2x^4right)^4+2x^10{left(-2x^2right)}^3+2{x}^2-5{left({x}^4right)}^3

$${ \left(-2 { x }^{ 4 } \right) }^{ 4 } +2 { x }^{ 10 } { \left(-2 { x }^{ 2 } \right) }^{ 3 } +2 { x }^{ 2 } -5 { \left( { x }^{ 4 } \right) }^{ 3 }$$

Evaluate

$$x^{2}\left(2-5x^{10}\right)$$

Solution Steps

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

$$\left(-2x^{4}\right)^{4}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

Expand \left(-2x^{4}\right)^{4}.

$$\left(-2\right)^{4}\left(x^{4}\right)^{4}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(-2\right)^{4}x^{16}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

Calculate -2 to the power of 4 and get 16.

$$16x^{16}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

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

$$16x^{16}+2x^{10}\left(-2\right)^{3}\left(x^{2}\right)^{3}+2x^{2}-5x^{12}$$

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

$$16x^{16}+2x^{10}\left(-2\right)^{3}x^{6}+2x^{2}-5x^{12}$$

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

$$16x^{16}+2x^{10}\left(-8\right)x^{6}+2x^{2}-5x^{12}$$

Multiply 2 and -8 to get -16.

$$16x^{16}-16x^{10}x^{6}+2x^{2}-5x^{12}$$

To multiply powers of the same base, add their exponents. Add 10 and 6 to get 16.

$$16x^{16}-16x^{16}+2x^{2}-5x^{12}$$

Combine 16x^{16} and -16x^{16} to get 0.

$$2x^{2}-5x^{12}$$

Expand

$$2x^{2}-5x^{12}$$

Solution Steps

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

$$\left(-2x^{4}\right)^{4}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

Expand \left(-2x^{4}\right)^{4}.

$$\left(-2\right)^{4}\left(x^{4}\right)^{4}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(-2\right)^{4}x^{16}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

Calculate -2 to the power of 4 and get 16.

$$16x^{16}+2x^{10}\left(-2x^{2}\right)^{3}+2x^{2}-5x^{12}$$

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

$$16x^{16}+2x^{10}\left(-2\right)^{3}\left(x^{2}\right)^{3}+2x^{2}-5x^{12}$$

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

$$16x^{16}+2x^{10}\left(-2\right)^{3}x^{6}+2x^{2}-5x^{12}$$

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

$$16x^{16}+2x^{10}\left(-8\right)x^{6}+2x^{2}-5x^{12}$$

Multiply 2 and -8 to get -16.

$$16x^{16}-16x^{10}x^{6}+2x^{2}-5x^{12}$$

To multiply powers of the same base, add their exponents. Add 10 and 6 to get 16.

$$16x^{16}-16x^{16}+2x^{2}-5x^{12}$$

Combine 16x^{16} and -16x^{16} to get 0.

$$2x^{2}-5x^{12}$$