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

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

Evaluate

$$-3y^{8}x^{13}$$

Solution Steps

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

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

Expand \left(\left(-x^{2}\right)y\right)^{6}.

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

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

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

Expand \left(-x^{2}\right)^{6}.

$$3\left(-1\right)^{6}\left(x^{2}\right)^{6}y^{8}\left(-1\right)x$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$3\left(-1\right)^{6}x^{12}y^{8}\left(-1\right)x$$

Calculate -1 to the power of 6 and get 1.

$$3\times 1x^{12}y^{8}\left(-1\right)x$$

Multiply 3 and 1 to get 3.

$$3x^{12}y^{8}\left(-1\right)x$$

Multiply 3 and -1 to get -3.

$$-3x^{12}y^{8}x$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$-3x^{13}y^{8}$$

Expand

$$-3y^{8}x^{13}$$

Solution Steps

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

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

Expand \left(\left(-x^{2}\right)y\right)^{6}.

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

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

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

Expand \left(-x^{2}\right)^{6}.

$$3\left(-1\right)^{6}\left(x^{2}\right)^{6}y^{8}\left(-1\right)x$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$3\left(-1\right)^{6}x^{12}y^{8}\left(-1\right)x$$

Calculate -1 to the power of 6 and get 1.

$$3\times 1x^{12}y^{8}\left(-1\right)x$$

Multiply 3 and 1 to get 3.

$$3x^{12}y^{8}\left(-1\right)x$$

Multiply 3 and -1 to get -3.

$$-3x^{12}y^{8}x$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$-3x^{13}y^{8}$$