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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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