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

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

Evaluate

$$\left(xy\right)^{4}$$

Solution Steps

Expand \left(x^{-3}y^{2}\right)^{-4}.

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

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

$$\frac{x^{12}\left(y^{2}\right)^{-4}}{\left(y^{6}x^{-4}\right)^{-2}}$$

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

$$\frac{x^{12}y^{-8}}{\left(y^{6}x^{-4}\right)^{-2}}$$

Expand \left(y^{6}x^{-4}\right)^{-2}.

$$\frac{x^{12}y^{-8}}{\left(y^{6}\right)^{-2}\left(x^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{x^{12}y^{-8}}{y^{-12}\left(x^{-4}\right)^{-2}}$$

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

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

Cancel out x^{8} in both numerator and denominator.

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

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

$$x^{4}y^{4}$$

Expand

$$\left(xy\right)^{4}$$

Solution Steps

Expand \left(x^{-3}y^{2}\right)^{-4}.

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

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

$$\frac{x^{12}\left(y^{2}\right)^{-4}}{\left(y^{6}x^{-4}\right)^{-2}}$$

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

$$\frac{x^{12}y^{-8}}{\left(y^{6}x^{-4}\right)^{-2}}$$

Expand \left(y^{6}x^{-4}\right)^{-2}.

$$\frac{x^{12}y^{-8}}{\left(y^{6}\right)^{-2}\left(x^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{x^{12}y^{-8}}{y^{-12}\left(x^{-4}\right)^{-2}}$$

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

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

Cancel out x^{8} in both numerator and denominator.

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

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

$$x^{4}y^{4}$$