Numerical Equality: Finding the Expression Equal to 100

Which of the following clauses is equal to 100?

To determine which expression equals 100, we need to evaluate each option:

• Option 1: $5^2\cdot5$
  - Calculate $5^2 = 25$.
  - Then compute $25 \cdot 5 = 125$.
• Option 2: $4^2\cdot4$
  - Calculate $4^2 = 16$.
  - Then compute $16 \cdot 4 = 64$.
• Option 3: $25^4$
  - Calculate $(25^4)$, which simplified through breakdown is larger than 100 because $25^2 = 625$. Hence this 25 to the power of 4 will definitely be much larger than 100.
• Option 4: $5^2\cdot2^2$
  - Calculate $5^2 = 25$.
  - Calculate $2^2 = 4$.
  - Compute $25 \cdot 4 = 100$.

Therefore, the expression in Option 4, $5^2\cdot2^2$, equals 100. Thus, the correct choice is 4.

Thus, the clause that equals 100 is $5^2\cdot2^2$.