Solve left(2x^2right)^3left(-3xyright)^3

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

Evaluate

$$-216y^{3}x^{9}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

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

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

Calculate -3 to the power of 3 and get -27.

$$8x^{6}\left(-27\right)x^{3}y^{3}$$

Multiply 8 and -27 to get -216.

$$-216x^{6}x^{3}y^{3}$$

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

$$-216x^{9}y^{3}$$

Expand

$$-216y^{3}x^{9}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

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

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

Calculate -3 to the power of 3 and get -27.

$$8x^{6}\left(-27\right)x^{3}y^{3}$$

Multiply 8 and -27 to get -216.

$$-216x^{6}x^{3}y^{3}$$

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

$$-216x^{9}y^{3}$$