Find the Missing Exponent: (1/5)^□ = (1/5) × (1/5) × (1/5) × (1/5) × (1/5)

Question

Fill in the missing number:

15=1515151515 \frac{1}{5}^☐=\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}

Video Solution

Step-by-Step Solution

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

  • Step 1: Count the number of times 15 \frac{1}{5} is used as a factor in the product given.
  • Step 2: Use this count as the exponent in the expression 15 \frac{1}{5}^☐ .

Now, let's work through each step:
Step 1: The expression 1515151515 \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} shows that the base 15 \frac{1}{5} is used 5 times.
Step 2: Therefore, the exponent that makes the expression (15) \left( \frac{1}{5} \right)^☐ equal to the product is 5.

Therefore, the missing number in the expression 15 \frac{1}{5}^☐ is 5 5 .

Answer

5