Question

Evaluate the expression. $$\left(\frac{1}{5}\right)^{4}$$

Short answer

The evaluated expression of \( \left(\frac{1}{5}\right)^{4} \) is \( \frac{1}{625} \)

Step-by-step solution

Identify the base and the exponent

In the given expression \(\left(\frac{1}{5}\right)^{4}\), the base is \(\frac{1}{5}\) and the exponent 4. Therefore we must multiply the base 4 times.

Multiply the base

As described above, we need to multiply the base, which is \(\frac{1}{5}\) four times: \(\left(\frac{1}{5}\right)^{4} = \frac{1}{5} * \frac{1}{5} * \frac{1}{5} * \frac{1}{5}\).

Evaluate the multiplication

On multiplying the fractions we get: \(\frac{1}{5} * \frac{1}{5} * \frac{1}{5} * \frac{1}{5} = \frac{1}{625}\)