Compare Powers: Which is Greater, 5² or 2⁵?

Question

Which is larger?

52 ——25 5^2\text{ }_{——}2^5

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Calculate 525^2.
  • Step 2: Calculate 252^5.
  • Step 3: Compare the results to determine which is larger.

Let's work through each step:
Step 1: Calculate 525^2.
52=5×5=255^2 = 5 \times 5 = 25.

Step 2: Calculate 252^5.
25=2×2×2×2×2=322^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32.

Step 3: Compare the results.
We have 52=255^2 = 25 and 25=322^5 = 32. Clearly, 25<3225 < 32.

Therefore, 52 ——255^2 \text{ }_{——} 2^5 is < .

Answer

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