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

Fill in the missing number:

$x^☐=x\cdot x\cdot x\cdot x\cdot x\cdot x$

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

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

Now, let's work through these steps:

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

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

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

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