Solve for the Base: Finding the Number Whose Sixth Power Equals 2^6

Fill in the missing number:

$☐^6=2\cdot2\cdot2\cdot2\cdot2\cdot2$

To solve this problem, we have to determine the missing number in the expression $☐^6 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$.

Let's follow these steps:

• Step 1: Recognize that the right side of the equation, $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$, is equivalent to $2^6$, as it involves multiplying six 2s together.
• Step 2: The left side of the equation $☐^6$ means some number raised to the power of 6.
• Step 3: Since the two sides must be equal, we recognize that the base on both sides must be the same if the exponents are equal. Hence, the missing base number, represented by $☐$, is $2$.

When we match the two expressions based on exponents, we find that the correct base completing the equation $☐^6 = 2^6$ is $2$.

Therefore, the missing number is $\mathbf{2}$.