Solve x^10y^2/(x^3y)^4

$$\frac { x ^ { 10 } y ^ { 2 } } { ( x ^ { 3 } y ) ^ { 4 } }$$

Evaluate

$$\frac{1}{\left(xy\right)^{2}}$$

Solution Steps

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

$$\frac{x^{10}y^{2}}{\left(x^{3}\right)^{4}y^{4}}$$

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

$$\frac{x^{10}y^{2}}{x^{12}y^{4}}$$

Cancel out y^{2}x^{10} in both numerator and denominator.

$$\frac{1}{x^{2}y^{2}}$$

Expand

$$\frac{1}{\left(xy\right)^{2}}$$

Solution Steps

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

$$\frac{x^{10}y^{2}}{\left(x^{3}\right)^{4}y^{4}}$$

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

$$\frac{x^{10}y^{2}}{x^{12}y^{4}}$$

Cancel out y^{2}x^{10} in both numerator and denominator.

$$\frac{1}{x^{2}y^{2}}$$