Solve (-2x^{3}z^{3})^3(3x^2y^2z^4)

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

Evaluate

$$-24y^{2}x^{11}z^{13}$$

Solution Steps

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

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$-8x^{9}z^{9}\times 3x^{2}y^{2}z^{4}$$

Multiply -8 and 3 to get -24.

$$-24x^{9}z^{9}x^{2}y^{2}z^{4}$$

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

$$-24x^{11}z^{9}y^{2}z^{4}$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$-24x^{11}z^{13}y^{2}$$

Expand

$$-24y^{2}x^{11}z^{13}$$

Solution Steps

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

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$-8x^{9}z^{9}\times 3x^{2}y^{2}z^{4}$$

Multiply -8 and 3 to get -24.

$$-24x^{9}z^{9}x^{2}y^{2}z^{4}$$

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

$$-24x^{11}z^{9}y^{2}z^{4}$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$-24x^{11}z^{13}y^{2}$$