Solve (-4a^2/6bc^4)^2

$$( - \frac { 4 a ^ { 2 } } { 6 b c ^ { 4 } } ) ^ { 2 }$$

Evaluate

$$\frac{4a^{4}}{9b^{2}c^{8}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(-\frac{2a^{2}}{3bc^{4}}\right)^{2}$$

Calculate -\frac{2a^{2}}{3bc^{4}} to the power of 2 and get \left(\frac{2a^{2}}{3bc^{4}}\right)^{2}.

$$\left(\frac{2a^{2}}{3bc^{4}}\right)^{2}$$

To raise \frac{2a^{2}}{3bc^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{2}\right)^{2}}{\left(3bc^{4}\right)^{2}}$$

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

$$\frac{2^{2}\left(a^{2}\right)^{2}}{\left(3bc^{4}\right)^{2}}$$

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

$$\frac{2^{2}a^{4}}{\left(3bc^{4}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}}{\left(3bc^{4}\right)^{2}}$$

Expand \left(3bc^{4}\right)^{2}.

$$\frac{4a^{4}}{3^{2}b^{2}\left(c^{4}\right)^{2}}$$

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

$$\frac{4a^{4}}{3^{2}b^{2}c^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4a^{4}}{9b^{2}c^{8}}$$

Expand

$$\frac{4a^{4}}{9b^{2}c^{8}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(-\frac{2a^{2}}{3bc^{4}}\right)^{2}$$

Calculate -\frac{2a^{2}}{3bc^{4}} to the power of 2 and get \left(\frac{2a^{2}}{3bc^{4}}\right)^{2}.

$$\left(\frac{2a^{2}}{3bc^{4}}\right)^{2}$$

To raise \frac{2a^{2}}{3bc^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{2}\right)^{2}}{\left(3bc^{4}\right)^{2}}$$

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

$$\frac{2^{2}\left(a^{2}\right)^{2}}{\left(3bc^{4}\right)^{2}}$$

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

$$\frac{2^{2}a^{4}}{\left(3bc^{4}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}}{\left(3bc^{4}\right)^{2}}$$

Expand \left(3bc^{4}\right)^{2}.

$$\frac{4a^{4}}{3^{2}b^{2}\left(c^{4}\right)^{2}}$$

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

$$\frac{4a^{4}}{3^{2}b^{2}c^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4a^{4}}{9b^{2}c^{8}}$$