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

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

Evaluate

$$-81z^{5}x^{11}y^{14}$$

Solution Steps

Expand \left(-3x^{2}y^{3}z\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\left(-x^{3}\right)y^{2}z\left(-3\right)^{4}x^{8}\left(y^{3}\right)^{4}z^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-x^{3}\right)y^{2}z\left(-3\right)^{4}x^{8}y^{12}z^{4}$$

Calculate -3 to the power of 4 and get 81.

$$\left(-x^{3}\right)y^{2}z\times 81x^{8}y^{12}z^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$\left(-x^{3}\right)y^{14}z\times 81x^{8}z^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\left(-x^{3}\right)y^{14}z^{5}\times 81x^{8}$$

Multiply -1 and 81 to get -81.

$$-81x^{3}y^{14}z^{5}x^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$-81x^{11}y^{14}z^{5}$$

Expand

$$-81z^{5}x^{11}y^{14}$$

Solution Steps

Expand \left(-3x^{2}y^{3}z\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\left(-x^{3}\right)y^{2}z\left(-3\right)^{4}x^{8}\left(y^{3}\right)^{4}z^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-x^{3}\right)y^{2}z\left(-3\right)^{4}x^{8}y^{12}z^{4}$$

Calculate -3 to the power of 4 and get 81.

$$\left(-x^{3}\right)y^{2}z\times 81x^{8}y^{12}z^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$\left(-x^{3}\right)y^{14}z\times 81x^{8}z^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\left(-x^{3}\right)y^{14}z^{5}\times 81x^{8}$$

Multiply -1 and 81 to get -81.

$$-81x^{3}y^{14}z^{5}x^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$-81x^{11}y^{14}z^{5}$$