Solve (5x^-4/6y^-4)^-2

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

Evaluate

$$\frac{36\times \left(\frac{x}{y}\right)^{8}}{25}$$

Solution Steps

To raise \frac{5x^{-4}}{6y^{-4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{5^{-2}x^{8}}{\left(6y^{-4}\right)^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{8}}{\left(6y^{-4}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}x^{8}}{6^{-2}\left(y^{-4}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}x^{8}}{6^{-2}y^{8}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{\frac{1}{25}x^{8}}{\frac{1}{36}y^{8}}$$

Expand

$$\frac{36\times \left(\frac{x}{y}\right)^{8}}{25}$$

Solution Steps

To raise \frac{5x^{-4}}{6y^{-4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{5^{-2}x^{8}}{\left(6y^{-4}\right)^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{8}}{\left(6y^{-4}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}x^{8}}{6^{-2}\left(y^{-4}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}x^{8}}{6^{-2}y^{8}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{\frac{1}{25}x^{8}}{\frac{1}{36}y^{8}}$$