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

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

Evaluate

$$-27z^{6}\left(xy\right)^{7}$$

Solution Steps

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

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

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

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

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

$$-3x^{3}yz^{4}\left(-3\right)^{2}x^{4}y^{6}z^{2}$$

Calculate -3 to the power of 2 and get 9.

$$-3x^{3}yz^{4}\times 9x^{4}y^{6}z^{2}$$

Multiply -3 and 9 to get -27.

$$-27x^{3}yz^{4}x^{4}y^{6}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-27x^{7}yz^{4}y^{6}z^{2}$$

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

$$-27x^{7}y^{7}z^{4}z^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-27x^{7}y^{7}z^{6}$$

Expand

$$-27z^{6}\left(xy\right)^{7}$$

Solution Steps

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

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

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

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

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

$$-3x^{3}yz^{4}\left(-3\right)^{2}x^{4}y^{6}z^{2}$$

Calculate -3 to the power of 2 and get 9.

$$-3x^{3}yz^{4}\times 9x^{4}y^{6}z^{2}$$

Multiply -3 and 9 to get -27.

$$-27x^{3}yz^{4}x^{4}y^{6}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-27x^{7}yz^{4}y^{6}z^{2}$$

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

$$-27x^{7}y^{7}z^{4}z^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-27x^{7}y^{7}z^{6}$$