Solve (frac{x^{-4}y^-7}{x^-2y^-5})^-2=

$$( \frac { x ^ { - 4 } y ^ { - 7 } } { x ^ { - 2 } y ^ { - 5 } } ) ^ { - 2 } =$$

Evaluate

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

Solution Steps

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

$$\left(\frac{1}{x^{2}y^{2}}\right)^{-2}$$

To raise \frac{1}{x^{2}y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(x^{2}y^{2}\right)^{-2}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{1}{\left(x^{2}y^{2}\right)^{-2}}$$

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

$$\frac{1}{\left(x^{2}\right)^{-2}\left(y^{2}\right)^{-2}}$$

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

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

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

$$\frac{1}{x^{-4}y^{-4}}$$

Expand

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

Solution Steps

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

$$\left(\frac{1}{x^{2}y^{2}}\right)^{-2}$$

To raise \frac{1}{x^{2}y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(x^{2}y^{2}\right)^{-2}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{1}{\left(x^{2}y^{2}\right)^{-2}}$$

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

$$\frac{1}{\left(x^{2}\right)^{-2}\left(y^{2}\right)^{-2}}$$

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

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

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

$$\frac{1}{x^{-4}y^{-4}}$$