Solve x^□ = x×x×x×x×x×x: Finding the Missing Exponent

Question

Fill in the missing number:

x=xxxxxx x^☐=x\cdot x\cdot x\cdot x\cdot x\cdot x

Video Solution

Step-by-Step Solution

To solve this problem, we'll adopt the following method:

  • Step 1: Understand the given expression in multiplication form: xxxxxx x \cdot x \cdot x \cdot x \cdot x \cdot x .
  • Step 2: Count the number of times x x appears.
  • Step 3: Determine that the expression is equivalent to xn x^n , where n n is the count of x x factors.

Now, let's work through these steps:

Step 1: We are given the product xxxxxx x \cdot x \cdot x \cdot x \cdot x \cdot x , which is clearly a multiplication of x x six times.

Step 2: Counting these, we see that x x appears 6 times.

Step 3: Therefore, the product can be expressed as x6 x^6 , meaning that the expression x=xxxxxx x^☐ = x \cdot x \cdot x \cdot x \cdot x \cdot x implies that =6 ☑ = 6 .

Thus, the missing number is 6, corresponding to choice 2.

Answer

6