Solve 3xy^4left(-x^2yright)^3

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

Evaluate

$$-3\left(xy\right)^{7}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$3xy^{7}\left(-x^{2}\right)^{3}$$

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

$$3xy^{7}\left(-1\right)^{3}\left(x^{2}\right)^{3}$$

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

$$3xy^{7}\left(-1\right)^{3}x^{6}$$

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

$$3xy^{7}\left(-1\right)x^{6}$$

Multiply 3 and -1 to get -3.

$$-3xy^{7}x^{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$-3x^{7}y^{7}$$

Expand

$$-3\left(xy\right)^{7}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$3xy^{7}\left(-x^{2}\right)^{3}$$

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

$$3xy^{7}\left(-1\right)^{3}\left(x^{2}\right)^{3}$$

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

$$3xy^{7}\left(-1\right)^{3}x^{6}$$

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

$$3xy^{7}\left(-1\right)x^{6}$$

Multiply 3 and -1 to get -3.

$$-3xy^{7}x^{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$-3x^{7}y^{7}$$