Solve frac{3x^{2}y^{2}z^{2}}{(2x^2y^3z^2)^3}

$$\frac { 3 x ^ { 2 } y ^ { 2 } z ^ { 2 } } { ( 2 x ^ { 2 } y ^ { 3 } z ^ { 2 } ) ^ { 3 } }$$

Evaluate

$$\frac{3}{8y^{7}\left(xz\right)^{4}}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{3x^{2}y^{2}z^{2}}{2^{3}x^{6}y^{9}z^{6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{3x^{2}y^{2}z^{2}}{8x^{6}y^{9}z^{6}}$$

Cancel out x^{2}y^{2}z^{2} in both numerator and denominator.

$$\frac{3}{8x^{4}z^{4}y^{7}}$$

Expand

$$\frac{3}{8y^{7}\left(xz\right)^{4}}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{3x^{2}y^{2}z^{2}}{2^{3}x^{6}y^{9}z^{6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{3x^{2}y^{2}z^{2}}{8x^{6}y^{9}z^{6}}$$

Cancel out x^{2}y^{2}z^{2} in both numerator and denominator.

$$\frac{3}{8x^{4}z^{4}y^{7}}$$