Solve frac{(x^{3}y^{2})^3}{(x^4y^3)^5}

$$\frac { ( x ^ { 3 } y ^ { 2 } ) ^ { 3 } } { ( x ^ { 4 } y ^ { 3 } ) ^ { 5 } }$$

Evaluate

$$\frac{1}{y^{9}x^{11}}$$

Solution Steps

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

$$\frac{\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}}{\left(x^{4}y^{3}\right)^{5}}$$

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

$$\frac{x^{9}\left(y^{2}\right)^{3}}{\left(x^{4}y^{3}\right)^{5}}$$

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

$$\frac{x^{9}y^{6}}{\left(x^{4}y^{3}\right)^{5}}$$

Expand \left(x^{4}y^{3}\right)^{5}.

$$\frac{x^{9}y^{6}}{\left(x^{4}\right)^{5}\left(y^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{x^{9}y^{6}}{x^{20}\left(y^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{x^{9}y^{6}}{x^{20}y^{15}}$$

Cancel out y^{6}x^{9} in both numerator and denominator.

$$\frac{1}{y^{9}x^{11}}$$

Expand

$$\frac{1}{y^{9}x^{11}}$$

Solution Steps

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

$$\frac{\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}}{\left(x^{4}y^{3}\right)^{5}}$$

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

$$\frac{x^{9}\left(y^{2}\right)^{3}}{\left(x^{4}y^{3}\right)^{5}}$$

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

$$\frac{x^{9}y^{6}}{\left(x^{4}y^{3}\right)^{5}}$$

Expand \left(x^{4}y^{3}\right)^{5}.

$$\frac{x^{9}y^{6}}{\left(x^{4}\right)^{5}\left(y^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{x^{9}y^{6}}{x^{20}\left(y^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{x^{9}y^{6}}{x^{20}y^{15}}$$

Cancel out y^{6}x^{9} in both numerator and denominator.

$$\frac{1}{y^{9}x^{11}}$$