Solve frac{(x^{4}y^{4})^{4}(xy^4)^-4}{x^4y^5}

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

Evaluate

$$\frac{x^{8}}{y^{5}}$$

Solution Steps

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

$$\frac{\left(x^{4}\right)^{4}\left(y^{4}\right)^{4}\left(xy^{4}\right)^{-4}}{x^{4}y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{x^{16}\left(y^{4}\right)^{4}\left(xy^{4}\right)^{-4}}{x^{4}y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{x^{16}y^{16}\left(xy^{4}\right)^{-4}}{x^{4}y^{5}}$$

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

$$\frac{x^{16}y^{16}x^{-4}\left(y^{4}\right)^{-4}}{x^{4}y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$\frac{x^{16}y^{16}x^{-4}y^{-16}}{x^{4}y^{5}}$$

To multiply powers of the same base, add their exponents. Add 16 and -4 to get 12.

$$\frac{x^{12}y^{16}y^{-16}}{x^{4}y^{5}}$$

Multiply y^{16} and y^{-16} to get 1.

$$\frac{x^{12}}{x^{4}y^{5}}$$

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

$$\frac{x^{8}}{y^{5}}$$

Expand

$$\frac{x^{8}}{y^{5}}$$

Solution Steps

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

$$\frac{\left(x^{4}\right)^{4}\left(y^{4}\right)^{4}\left(xy^{4}\right)^{-4}}{x^{4}y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{x^{16}\left(y^{4}\right)^{4}\left(xy^{4}\right)^{-4}}{x^{4}y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{x^{16}y^{16}\left(xy^{4}\right)^{-4}}{x^{4}y^{5}}$$

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

$$\frac{x^{16}y^{16}x^{-4}\left(y^{4}\right)^{-4}}{x^{4}y^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$\frac{x^{16}y^{16}x^{-4}y^{-16}}{x^{4}y^{5}}$$

To multiply powers of the same base, add their exponents. Add 16 and -4 to get 12.

$$\frac{x^{12}y^{16}y^{-16}}{x^{4}y^{5}}$$

Multiply y^{16} and y^{-16} to get 1.

$$\frac{x^{12}}{x^{4}y^{5}}$$

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

$$\frac{x^{8}}{y^{5}}$$