Solve (w^2/2u^4)^4

$$( \frac { w ^ { 2 } } { 2 u ^ { 4 } } ) ^ { 4 }$$

Evaluate

$$\frac{w^{8}}{16u^{16}}$$

Solution Steps

To raise \frac{w^{2}}{2u^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(w^{2}\right)^{4}}{\left(2u^{4}\right)^{4}}$$

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

$$\frac{w^{8}}{\left(2u^{4}\right)^{4}}$$

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

$$\frac{w^{8}}{2^{4}\left(u^{4}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{w^{8}}{2^{4}u^{16}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{w^{8}}{16u^{16}}$$

Expand

$$\frac{w^{8}}{16u^{16}}$$

Solution Steps

To raise \frac{w^{2}}{2u^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(w^{2}\right)^{4}}{\left(2u^{4}\right)^{4}}$$

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

$$\frac{w^{8}}{\left(2u^{4}\right)^{4}}$$

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

$$\frac{w^{8}}{2^{4}\left(u^{4}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{w^{8}}{2^{4}u^{16}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{w^{8}}{16u^{16}}$$