Solve (z^-6/2y^2)^-4

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

Evaluate

$$16y^{8}z^{24}$$

Solution Steps

To raise \frac{z^{-6}}{2y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -6 and -4 to get 24.

$$\frac{z^{24}}{\left(2y^{2}\right)^{-4}}$$

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

$$\frac{z^{24}}{2^{-4}\left(y^{2}\right)^{-4}}$$

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

$$\frac{z^{24}}{2^{-4}y^{-8}}$$

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

$$\frac{z^{24}}{\frac{1}{16}y^{-8}}$$

Expand

$$16y^{8}z^{24}$$

Solution Steps

To raise \frac{z^{-6}}{2y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -6 and -4 to get 24.

$$\frac{z^{24}}{\left(2y^{2}\right)^{-4}}$$

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

$$\frac{z^{24}}{2^{-4}\left(y^{2}\right)^{-4}}$$

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

$$\frac{z^{24}}{2^{-4}y^{-8}}$$

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

$$\frac{z^{24}}{\frac{1}{16}y^{-8}}$$