Solve frac{(x^{4}y^{4})^{3}(xy^3)^-4}{x^4y^6}

$$\frac { ( x ^ { 4 } y ^ { 4 } ) ^ { 3 } ( x y ^ { 3 } ) ^ { - 4 } } { x ^ { 4 } y ^ { 6 } }$$

Evaluate

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

Solution Steps

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

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

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

$$\frac{x^{12}\left(y^{4}\right)^{3}\left(xy^{3}\right)^{-4}}{x^{4}y^{6}}$$

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

$$\frac{x^{12}y^{12}\left(xy^{3}\right)^{-4}}{x^{4}y^{6}}$$

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

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

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

$$\frac{x^{12}y^{12}x^{-4}y^{-12}}{x^{4}y^{6}}$$

To multiply powers of the same base, add their exponents. Add 12 and -4 to get 8.

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

Multiply y^{12} and y^{-12} to get 1.

$$\frac{x^{8}}{x^{4}y^{6}}$$

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

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

Expand

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

Solution Steps

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

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

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

$$\frac{x^{12}\left(y^{4}\right)^{3}\left(xy^{3}\right)^{-4}}{x^{4}y^{6}}$$

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

$$\frac{x^{12}y^{12}\left(xy^{3}\right)^{-4}}{x^{4}y^{6}}$$

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

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

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

$$\frac{x^{12}y^{12}x^{-4}y^{-12}}{x^{4}y^{6}}$$

To multiply powers of the same base, add their exponents. Add 12 and -4 to get 8.

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

Multiply y^{12} and y^{-12} to get 1.

$$\frac{x^{8}}{x^{4}y^{6}}$$

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

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