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

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

Evaluate

$$9z^{4}y^{6}x^{14}$$

Solution Steps

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

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

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(x^{3}\right)^{2}z^{2}\times 3^{2}x^{8}\left(y^{3}\right)^{2}z^{2}$$

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$x^{14}z^{4}\times 9y^{6}$$

Expand

$$9z^{4}y^{6}x^{14}$$

Solution Steps

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

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

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(x^{3}\right)^{2}z^{2}\times 3^{2}x^{8}\left(y^{3}\right)^{2}z^{2}$$

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$x^{14}z^{4}\times 9y^{6}$$