Solve (-xy^3)^3(4x^3y)^2

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

Evaluate

$$-16x^{9}y^{11}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-x\right)^{3}y^{9}\times \left(4x^{3}y\right)^{2}$$

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

$$\left(-x\right)^{3}y^{9}\times 4^{2}\left(x^{3}\right)^{2}y^{2}$$

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

$$\left(-x\right)^{3}y^{9}\times 4^{2}x^{6}y^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\left(-x\right)^{3}y^{9}\times 16x^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$\left(-x\right)^{3}y^{11}\times 16x^{6}$$

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

$$\left(-1\right)^{3}x^{3}y^{11}\times 16x^{6}$$

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

$$-x^{3}y^{11}\times 16x^{6}$$

Multiply -1 and 16 to get -16.

$$-16x^{3}y^{11}x^{6}$$

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

$$-16x^{9}y^{11}$$

Expand

$$-16x^{9}y^{11}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-x\right)^{3}y^{9}\times \left(4x^{3}y\right)^{2}$$

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

$$\left(-x\right)^{3}y^{9}\times 4^{2}\left(x^{3}\right)^{2}y^{2}$$

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

$$\left(-x\right)^{3}y^{9}\times 4^{2}x^{6}y^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\left(-x\right)^{3}y^{9}\times 16x^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$\left(-x\right)^{3}y^{11}\times 16x^{6}$$

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

$$\left(-1\right)^{3}x^{3}y^{11}\times 16x^{6}$$

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

$$-x^{3}y^{11}\times 16x^{6}$$

Multiply -1 and 16 to get -16.

$$-16x^{3}y^{11}x^{6}$$

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

$$-16x^{9}y^{11}$$