Solve (-3xy^4z)^3(3y^2z^3)

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

Evaluate

$$-81x^{3}z^{6}y^{14}$$

Solution Steps

Expand \left(-3xy^{4}z\right)^{3}.

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

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

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

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

$$-27x^{3}y^{12}z^{3}\times 3y^{2}z^{3}$$

Multiply -27 and 3 to get -81.

$$-81x^{3}y^{12}z^{3}y^{2}z^{3}$$

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

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

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

$$-81x^{3}y^{14}z^{6}$$

Expand

$$-81x^{3}z^{6}y^{14}$$

Solution Steps

Expand \left(-3xy^{4}z\right)^{3}.

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

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

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

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

$$-27x^{3}y^{12}z^{3}\times 3y^{2}z^{3}$$

Multiply -27 and 3 to get -81.

$$-81x^{3}y^{12}z^{3}y^{2}z^{3}$$

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

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

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

$$-81x^{3}y^{14}z^{6}$$