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

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

Evaluate

$$\frac{x^{12}}{y^{36}}$$

Solution Steps

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

$$\left(\frac{x^{-2}y^{12}}{x^{2}}\right)^{-3}$$

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

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

To raise \frac{y^{12}}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 12 and -3 to get -36.

$$\frac{y^{-36}}{\left(x^{4}\right)^{-3}}$$

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

$$\frac{y^{-36}}{x^{-12}}$$

Expand

$$\frac{x^{12}}{y^{36}}$$

Solution Steps

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

$$\left(\frac{x^{-2}y^{12}}{x^{2}}\right)^{-3}$$

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

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

To raise \frac{y^{12}}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 12 and -3 to get -36.

$$\frac{y^{-36}}{\left(x^{4}\right)^{-3}}$$

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

$$\frac{y^{-36}}{x^{-12}}$$