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

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

Evaluate

$$-\left(xy\right)^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$x^{6}y^{9}\left(-x\right)^{3}$$

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

$$x^{6}y^{9}\left(-1\right)^{3}x^{3}$$

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

$$x^{6}y^{9}\left(-1\right)x^{3}$$

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

$$x^{9}y^{9}\left(-1\right)$$

Expand

$$-\left(xy\right)^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$x^{6}y^{9}\left(-x\right)^{3}$$

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

$$x^{6}y^{9}\left(-1\right)^{3}x^{3}$$

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

$$x^{6}y^{9}\left(-1\right)x^{3}$$

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

$$x^{9}y^{9}\left(-1\right)$$