Solve (2x^3y)^2(-xy^2)^3

$$( 2 x ^ { 3 } y ) ^ { 2 } ( - x y ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-4y^{8}x^{9}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

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

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

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

$$4x^{6}y^{8}\left(-1\right)^{3}x^{3}$$

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

$$4x^{6}y^{8}\left(-1\right)x^{3}$$

Multiply 4 and -1 to get -4.

$$-4x^{6}y^{8}x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-4x^{9}y^{8}$$

Expand

$$-4y^{8}x^{9}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

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

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

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

$$4x^{6}y^{8}\left(-1\right)^{3}x^{3}$$

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

$$4x^{6}y^{8}\left(-1\right)x^{3}$$

Multiply 4 and -1 to get -4.

$$-4x^{6}y^{8}x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-4x^{9}y^{8}$$