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

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

Evaluate

$$\frac{16}{y^{8}x^{20}}$$

Solution Steps

To raise \frac{x^{5}}{2y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{x^{-20}}{2^{-4}y^{8}}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\frac{x^{-20}}{\frac{1}{16}y^{8}}$$

Expand

$$\frac{16}{y^{8}x^{20}}$$

Solution Steps

To raise \frac{x^{5}}{2y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{x^{-20}}{2^{-4}y^{8}}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\frac{x^{-20}}{\frac{1}{16}y^{8}}$$