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

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

Evaluate

$$-72y^{10}x^{13}z^{18}$$

Solution Steps

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

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

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

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

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

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

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

$$\left(-2\right)^{3}x^{9}y^{6}z^{12}\left(-3x^{2}y^{2}z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3x^{2}y^{2}z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\left(z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}x^{4}\left(y^{2}\right)^{2}\left(z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}x^{4}y^{4}\left(z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}x^{4}y^{4}z^{6}$$

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

$$-8x^{9}y^{6}z^{12}\times 9x^{4}y^{4}z^{6}$$

Multiply -8 and 9 to get -72.

$$-72x^{9}y^{6}z^{12}x^{4}y^{4}z^{6}$$

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

$$-72x^{13}y^{6}z^{12}y^{4}z^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$-72x^{13}y^{10}z^{12}z^{6}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$-72x^{13}y^{10}z^{18}$$

Expand

$$-72y^{10}x^{13}z^{18}$$

Solution Steps

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

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

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

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

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

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

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

$$\left(-2\right)^{3}x^{9}y^{6}z^{12}\left(-3x^{2}y^{2}z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3x^{2}y^{2}z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\left(z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}x^{4}\left(y^{2}\right)^{2}\left(z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}x^{4}y^{4}\left(z^{3}\right)^{2}$$

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

$$-8x^{9}y^{6}z^{12}\left(-3\right)^{2}x^{4}y^{4}z^{6}$$

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

$$-8x^{9}y^{6}z^{12}\times 9x^{4}y^{4}z^{6}$$

Multiply -8 and 9 to get -72.

$$-72x^{9}y^{6}z^{12}x^{4}y^{4}z^{6}$$

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

$$-72x^{13}y^{6}z^{12}y^{4}z^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$-72x^{13}y^{10}z^{12}z^{6}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$-72x^{13}y^{10}z^{18}$$