Solve for the Base: Finding x in x^7 = (1/5)^7

Fill in the missing number:

$☐^7=\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}$

To solve this problem, we'll begin by simplifying the expression on the right side of the equation:

$☐^7 = \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5}$

Using the laws of exponents, multiplying the fraction $\frac{1}{5}$ by itself seven times can be expressed as:

$\left(\frac{1}{5}\right)^7$

Now, the equation becomes:

$☐^7 = \left(\frac{1}{5}\right)^7$

Since the exponents on both sides of the equation are the same, the bases must be equal as well. Therefore, $☐ = \frac{1}{5}$.

Thus, the missing number is:

$\frac{1}{5}$