Solve (a/2a^3)^5

$$( \frac { a } { 2 a ^ { 3 } } ) ^ { 5 }$$

Evaluate

$$\frac{1}{32a^{10}}$$

Solution Steps

Cancel out a in both numerator and denominator.

$$\left(\frac{1}{2a^{2}}\right)^{5}$$

To raise \frac{1}{2a^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{5}}{\left(2a^{2}\right)^{5}}$$

Calculate 1 to the power of 5 and get 1.

$$\frac{1}{\left(2a^{2}\right)^{5}}$$

Expand \left(2a^{2}\right)^{5}.

$$\frac{1}{2^{5}\left(a^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{1}{2^{5}a^{10}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{1}{32a^{10}}$$

Expand

$$\frac{1}{32a^{10}}$$

Solution Steps

Cancel out a in both numerator and denominator.

$$\left(\frac{1}{2a^{2}}\right)^{5}$$

To raise \frac{1}{2a^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{5}}{\left(2a^{2}\right)^{5}}$$

Calculate 1 to the power of 5 and get 1.

$$\frac{1}{\left(2a^{2}\right)^{5}}$$

Expand \left(2a^{2}\right)^{5}.

$$\frac{1}{2^{5}\left(a^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{1}{2^{5}a^{10}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{1}{32a^{10}}$$