Solve (2a^2/a^5)^6

$$( \frac { 2 a ^ { 2 } } { a ^ { 5 } } ) ^ { 6 }$$

Evaluate

$$\frac{64}{a^{18}}$$

Solution Steps

Cancel out a^{2} in both numerator and denominator.

$$\left(\frac{2}{a^{3}}\right)^{6}$$

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

$$\frac{2^{6}}{\left(a^{3}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{2^{6}}{a^{18}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{64}{a^{18}}$$

Expand

$$\frac{64}{a^{18}}$$

Solution Steps

Cancel out a^{2} in both numerator and denominator.

$$\left(\frac{2}{a^{3}}\right)^{6}$$

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

$$\frac{2^{6}}{\left(a^{3}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{2^{6}}{a^{18}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{64}{a^{18}}$$