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

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

Evaluate

$$\frac{1}{x^{5}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{x^{4}y^{6}}{x^{9}y^{6}}$$

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

$$\frac{1}{x^{5}}$$

Expand

$$\frac{1}{x^{5}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{x^{4}y^{6}}{x^{9}y^{6}}$$

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

$$\frac{1}{x^{5}}$$