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

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

Evaluate

$$-24x^{7}y^{11}$$

Solution Steps

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

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

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

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

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

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

Calculate 2 to the power of 3 and get 8.

$$8x^{6}y^{9}\left(-3\right)y^{2}x$$

Multiply 8 and -3 to get -24.

$$-24x^{6}y^{9}y^{2}x$$

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

$$-24x^{6}y^{11}x$$

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

$$-24x^{7}y^{11}$$

Expand

$$-24x^{7}y^{11}$$

Solution Steps

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

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

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

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

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

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

Calculate 2 to the power of 3 and get 8.

$$8x^{6}y^{9}\left(-3\right)y^{2}x$$

Multiply 8 and -3 to get -24.

$$-24x^{6}y^{9}y^{2}x$$

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

$$-24x^{6}y^{11}x$$

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

$$-24x^{7}y^{11}$$