Expression Comparison: Finding the Highest Value Among Mathematical Expressions

To solve this problem, we shall compute the value of each expression:

• First, calculate $12^4$:
  $12^4 = 12 \times 12 \times 12 \times 12 = 20736$.
• Next, calculate $9^4$:
  $9^4 = 9 \times 9 \times 9 \times 9 = 6561$.
• Then, calculate $5^6$:
  $5^6 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625$.
• Finally, calculate $3^5$:
  $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$.

After computing the values, we compare them:

• $12^4 = 20736$
• $9^4 = 6561$
• $5^6 = 15625$
• $3^5 = 243$

Among these, the highest value is $20736$, which corresponds to $12^4$.

Therefore, the expression with the highest value is $12^4$.