Solve (b^2/-2a^4)^4

$$( \frac { b ^ { 2 } } { - 2 a ^ { 4 } } ) ^ { 4 }$$

Evaluate

$$\frac{b^{8}}{16a^{16}}$$

Solution Steps

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

$$\frac{\left(b^{2}\right)^{4}}{\left(-2a^{4}\right)^{4}}$$

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

$$\frac{b^{8}}{\left(-2a^{4}\right)^{4}}$$

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

$$\frac{b^{8}}{\left(-2\right)^{4}\left(a^{4}\right)^{4}}$$

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

$$\frac{b^{8}}{\left(-2\right)^{4}a^{16}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{b^{8}}{16a^{16}}$$

Expand

$$\frac{b^{8}}{16a^{16}}$$

Solution Steps

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

$$\frac{\left(b^{2}\right)^{4}}{\left(-2a^{4}\right)^{4}}$$

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

$$\frac{b^{8}}{\left(-2a^{4}\right)^{4}}$$

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

$$\frac{b^{8}}{\left(-2\right)^{4}\left(a^{4}\right)^{4}}$$

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

$$\frac{b^{8}}{\left(-2\right)^{4}a^{16}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{b^{8}}{16a^{16}}$$