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

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

Evaluate

$$27z^{6}x^{8}y^{13}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{2}\right)y^{4}z^{3}\left(-3\right)^{3}x^{6}y^{9}z^{3}$$

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

$$\left(-x^{2}\right)y^{4}z^{3}\left(-27\right)x^{6}y^{9}z^{3}$$

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

$$\left(-x^{2}\right)y^{13}z^{3}\left(-27\right)x^{6}z^{3}$$

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

$$\left(-x^{2}\right)y^{13}z^{6}\left(-27\right)x^{6}$$

Multiply -1 and -27 to get 27.

$$27x^{2}y^{13}z^{6}x^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$27x^{8}y^{13}z^{6}$$

Expand

$$27z^{6}x^{8}y^{13}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{2}\right)y^{4}z^{3}\left(-3\right)^{3}x^{6}y^{9}z^{3}$$

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

$$\left(-x^{2}\right)y^{4}z^{3}\left(-27\right)x^{6}y^{9}z^{3}$$

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

$$\left(-x^{2}\right)y^{13}z^{3}\left(-27\right)x^{6}z^{3}$$

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

$$\left(-x^{2}\right)y^{13}z^{6}\left(-27\right)x^{6}$$

Multiply -1 and -27 to get 27.

$$27x^{2}y^{13}z^{6}x^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$27x^{8}y^{13}z^{6}$$