Solve 3x^3(-x^2yz^3)^3=

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

Evaluate

$$-3y^{3}\left(xz\right)^{9}$$

Solution Steps

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

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

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

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

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

$$3x^{3}\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{3}z^{9}$$

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

$$3x^{3}\left(-1\right)^{3}x^{6}y^{3}z^{9}$$

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

$$3x^{3}\left(-1\right)x^{6}y^{3}z^{9}$$

Multiply 3 and -1 to get -3.

$$-3x^{3}x^{6}y^{3}z^{9}$$

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

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

Expand

$$-3y^{3}\left(xz\right)^{9}$$

Solution Steps

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

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

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

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

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

$$3x^{3}\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{3}z^{9}$$

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

$$3x^{3}\left(-1\right)^{3}x^{6}y^{3}z^{9}$$

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

$$3x^{3}\left(-1\right)x^{6}y^{3}z^{9}$$

Multiply 3 and -1 to get -3.

$$-3x^{3}x^{6}y^{3}z^{9}$$

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

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