Solve (x^{2}y^{3})^4+(-2x^4y)^2y^10

$$( x ^ { 2 } y ^ { 3 } ) ^ { 4 } + ( - 2 x ^ { 4 } y ) ^ { 2 } y ^ { 10 }$$

Evaluate

$$5x^{8}y^{12}$$

Solution Steps

Expand \left(x^{2}y^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$x^{8}\left(y^{3}\right)^{4}+\left(-2x^{4}y\right)^{2}y^{10}$$

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

$$x^{8}y^{12}+\left(-2x^{4}y\right)^{2}y^{10}$$

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

$$x^{8}y^{12}+\left(-2\right)^{2}\left(x^{4}\right)^{2}y^{2}y^{10}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

$$x^{8}y^{12}+4x^{8}y^{2}y^{10}$$

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$x^{8}y^{12}+4x^{8}y^{12}$$

Combine x^{8}y^{12} and 4x^{8}y^{12} to get 5x^{8}y^{12}.

$$5x^{8}y^{12}$$

Expand

$$5x^{8}y^{12}$$

Solution Steps

Expand \left(x^{2}y^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$x^{8}\left(y^{3}\right)^{4}+\left(-2x^{4}y\right)^{2}y^{10}$$

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

$$x^{8}y^{12}+\left(-2x^{4}y\right)^{2}y^{10}$$

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

$$x^{8}y^{12}+\left(-2\right)^{2}\left(x^{4}\right)^{2}y^{2}y^{10}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

$$x^{8}y^{12}+4x^{8}y^{2}y^{10}$$

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$x^{8}y^{12}+4x^{8}y^{12}$$

Combine x^{8}y^{12} and 4x^{8}y^{12} to get 5x^{8}y^{12}.

$$5x^{8}y^{12}$$