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

Solution Steps

00:12 Let's find the missing number together.
00:15 We'll use the power formula.
00:18 It means any number, like X, raised to the power of N.
00:23 Is simply X multiplied by itself, N times. Got it?
00:30 Now, let's apply this in our exercise.
00:34 Remember, X is the number we're multiplying.
00:37 Let's count how many times, to find our unknown, N.
00:42 And there we have it! That's how we solve the problem.

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