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

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

Evaluate

$$648z^{4}y^{6}x^{18}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$81x^{12}z^{4}\times 2^{3}x^{6}\left(y^{2}\right)^{3}$$

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

$$81x^{12}z^{4}\times 2^{3}x^{6}y^{6}$$

Calculate 2 to the power of 3 and get 8.

$$81x^{12}z^{4}\times 8x^{6}y^{6}$$

Multiply 81 and 8 to get 648.

$$648x^{12}z^{4}x^{6}y^{6}$$

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

$$648x^{18}z^{4}y^{6}$$

Expand

$$648z^{4}y^{6}x^{18}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$81x^{12}z^{4}\times 2^{3}x^{6}\left(y^{2}\right)^{3}$$

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

$$81x^{12}z^{4}\times 2^{3}x^{6}y^{6}$$

Calculate 2 to the power of 3 and get 8.

$$81x^{12}z^{4}\times 8x^{6}y^{6}$$

Multiply 81 and 8 to get 648.

$$648x^{12}z^{4}x^{6}y^{6}$$

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

$$648x^{18}z^{4}y^{6}$$