Mathematical Expression Comparison: Determining the Greater Value

Let's solve the problem by evaluating each expression:

• Calculate $2^4$:
  $2^4 = 2 \times 2 \times 2 \times 2 = 16$.
• Calculate $3^7$:
  $3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187$.
• Calculate $10^2$:
  $10^2 = 10 \times 10 = 100$.
• Calculate $5^5$:
  $5^5 = 5 \times 5 \times 5 \times 5 \times 5 = 3125$.

Now, let's compare the computed values: $16$ (for $2^4$), $2187$ (for $3^7$), $100$ (for $10^2$), and $3125$ (for $5^5$).

Clearly, the value $3125$ is the largest among the values we've calculated.

Therefore, the expression with the greatest value is $5^5$.