Solve frac{(x^{-5}y^{2})^{-4}y^{3}}{(x^3y^-6)^-1x^4}

$$\frac { ( x ^ { - 5 } y ^ { 2 } ) ^ { - 4 } y ^ { 3 } } { ( x ^ { 3 } y ^ { - 6 } ) ^ { - 1 } x ^ { 4 } }$$

Evaluate

$$\frac{x^{19}}{y^{11}}$$

Solution Steps

Expand \left(x^{-5}y^{2}\right)^{-4}.

$$\frac{\left(x^{-5}\right)^{-4}\left(y^{2}\right)^{-4}y^{3}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

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

$$\frac{x^{20}\left(y^{2}\right)^{-4}y^{3}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.

$$\frac{x^{20}y^{-8}y^{3}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

To multiply powers of the same base, add their exponents. Add -8 and 3 to get -5.

$$\frac{x^{20}y^{-5}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

Expand \left(x^{3}y^{-6}\right)^{-1}.

$$\frac{x^{20}y^{-5}}{\left(x^{3}\right)^{-1}\left(y^{-6}\right)^{-1}x^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$\frac{x^{20}y^{-5}}{x^{-3}\left(y^{-6}\right)^{-1}x^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -1 to get 6.

$$\frac{x^{20}y^{-5}}{x^{-3}y^{6}x^{4}}$$

To multiply powers of the same base, add their exponents. Add -3 and 4 to get 1.

$$\frac{x^{20}y^{-5}}{x^{1}y^{6}}$$

Cancel out x in both numerator and denominator.

$$\frac{y^{-5}x^{19}}{y^{6}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{x^{19}}{y^{11}}$$

Expand

$$\frac{x^{19}}{y^{11}}$$

Solution Steps

Expand \left(x^{-5}y^{2}\right)^{-4}.

$$\frac{\left(x^{-5}\right)^{-4}\left(y^{2}\right)^{-4}y^{3}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

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

$$\frac{x^{20}\left(y^{2}\right)^{-4}y^{3}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.

$$\frac{x^{20}y^{-8}y^{3}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

To multiply powers of the same base, add their exponents. Add -8 and 3 to get -5.

$$\frac{x^{20}y^{-5}}{\left(x^{3}y^{-6}\right)^{-1}x^{4}}$$

Expand \left(x^{3}y^{-6}\right)^{-1}.

$$\frac{x^{20}y^{-5}}{\left(x^{3}\right)^{-1}\left(y^{-6}\right)^{-1}x^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$\frac{x^{20}y^{-5}}{x^{-3}\left(y^{-6}\right)^{-1}x^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -1 to get 6.

$$\frac{x^{20}y^{-5}}{x^{-3}y^{6}x^{4}}$$

To multiply powers of the same base, add their exponents. Add -3 and 4 to get 1.

$$\frac{x^{20}y^{-5}}{x^{1}y^{6}}$$

Cancel out x in both numerator and denominator.

$$\frac{y^{-5}x^{19}}{y^{6}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{x^{19}}{y^{11}}$$