Solve (4a^3/2b^4)^2

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

Evaluate

$$\frac{4a^{6}}{b^{8}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

$$\frac{\left(2a^{3}\right)^{2}}{b^{8}}$$

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

$$\frac{2^{2}\left(a^{3}\right)^{2}}{b^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}a^{6}}{b^{8}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{6}}{b^{8}}$$

Expand

$$\frac{4a^{6}}{b^{8}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

$$\frac{\left(2a^{3}\right)^{2}}{b^{8}}$$

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

$$\frac{2^{2}\left(a^{3}\right)^{2}}{b^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}a^{6}}{b^{8}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{6}}{b^{8}}$$