Solve (-2xy^{4}w^3)^2*(-x^2y)^3

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

Evaluate

$$-4w^{6}x^{8}y^{11}$$

Solution Steps

Expand \left(-2xy^{4}w^{3}\right)^{2}.

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

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

$$\left(-2\right)^{2}x^{2}y^{8}\left(w^{3}\right)^{2}\left(\left(-x^{2}\right)y\right)^{3}$$

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

$$\left(-2\right)^{2}x^{2}y^{8}w^{6}\left(\left(-x^{2}\right)y\right)^{3}$$

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

$$4x^{2}y^{8}w^{6}\left(\left(-x^{2}\right)y\right)^{3}$$

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

$$4x^{2}y^{8}w^{6}\left(-x^{2}\right)^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$4x^{2}y^{11}w^{6}\left(-x^{2}\right)^{3}$$

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

$$4x^{2}y^{11}w^{6}\left(-1\right)^{3}\left(x^{2}\right)^{3}$$

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

$$4x^{2}y^{11}w^{6}\left(-1\right)^{3}x^{6}$$

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

$$4x^{2}y^{11}w^{6}\left(-1\right)x^{6}$$

Multiply 4 and -1 to get -4.

$$-4x^{2}y^{11}w^{6}x^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-4x^{8}y^{11}w^{6}$$

Expand

$$-4w^{6}x^{8}y^{11}$$

Solution Steps

Expand \left(-2xy^{4}w^{3}\right)^{2}.

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

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

$$\left(-2\right)^{2}x^{2}y^{8}\left(w^{3}\right)^{2}\left(\left(-x^{2}\right)y\right)^{3}$$

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

$$\left(-2\right)^{2}x^{2}y^{8}w^{6}\left(\left(-x^{2}\right)y\right)^{3}$$

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

$$4x^{2}y^{8}w^{6}\left(\left(-x^{2}\right)y\right)^{3}$$

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

$$4x^{2}y^{8}w^{6}\left(-x^{2}\right)^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$4x^{2}y^{11}w^{6}\left(-x^{2}\right)^{3}$$

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

$$4x^{2}y^{11}w^{6}\left(-1\right)^{3}\left(x^{2}\right)^{3}$$

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

$$4x^{2}y^{11}w^{6}\left(-1\right)^{3}x^{6}$$

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

$$4x^{2}y^{11}w^{6}\left(-1\right)x^{6}$$

Multiply 4 and -1 to get -4.

$$-4x^{2}y^{11}w^{6}x^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-4x^{8}y^{11}w^{6}$$