Find the Exponent: Solving 1/a^□ = (1/a)×(1/a)×(1/a)×(1/a)×(1/a)×(1/a)

Fill in the missing number:

$\frac{1}{a}^☐=\frac{1}{a}\cdot\frac{1}{a}\cdot\frac{1}{a}\cdot\frac{1}{a}\cdot\frac{1}{a}\cdot\frac{1}{a}$

To solve this problem, we'll follow these steps:

• Step 1: Identify the structure of the exponentiation in the problem.
• Step 2: Count the number of terms multiplied on the right-hand side.
• Step 3: Equate the number of terms to the exponent, thereby finding the missing number.

Now, let's work through each step:

Step 1: The problem provides the expression: $\frac{1}{a}^☐$ on the left-hand side, and $\frac{1}{a} \cdot \frac{1}{a} \cdot \frac{1}{a} \cdot \frac{1}{a} \cdot \frac{1}{a} \cdot \frac{1}{a}$ on the right-hand side.

Step 2: Count the number of $\frac{1}{a}$ terms on the right. There are 6 terms.

Step 3: The property of exponents allows us to say $\left(\frac{1}{a}\right)^☐$ should equal to $\frac{1}{a}$ multiplied by itself 6 times. Thus, the exponent on the left, indicated by ☐, must match the count of the terms:

Therefore, the missing number for ☐ is $6$.