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

Question

Fill in the missing number:

1a☐=1a⋅1a⋅1a⋅1a⋅1a⋅1a \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}

Video Solution

Step-by-Step Solution

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: 1a☐ \frac{1}{a}^☐ on the left-hand side, and 1a⋅1a⋅1a⋅1a⋅1a⋅1a\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 1a\frac{1}{a} terms on the right. There are 6 terms.

Step 3: The property of exponents allows us to say (1a)☐\left(\frac{1}{a}\right)^☐ should equal to 1a\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 6 .

Answer

6

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