Solve frac{(xy^{2}z^{3})^4}{(x^2y^2z)^3}=

$$\frac { ( x y ^ { 2 } z ^ { 3 } ) ^ { 4 } } { ( x ^ { 2 } y ^ { 2 } z ) ^ { 3 } } =$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{x^{4}y^{8}z^{12}}{x^{6}y^{6}z^{3}}$$

Cancel out z^{3}x^{4}y^{6} in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{x^{4}y^{8}z^{12}}{x^{6}y^{6}z^{3}}$$

Cancel out z^{3}x^{4}y^{6} in both numerator and denominator.

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