Use the order of operations to simplify 7^2 - 72 / 6^2 * 9 - 6.

Step-by-step solution

1. 1

   Evaluate the exponents first. There are no brackets, so powers come next in the hierarchy:

   $7^{2}=49,\qquad 6^{2}=36,$

   giving $49-72\div 36\cdot 9-6$.

2. 2

   Recognise that division and multiplication share a rank. Neither outranks the other; they are performed in the order they appear, reading left to right. Here the division comes first:

   $72\div 36=2.$

   Multiplying $36\cdot 9=324$ first would give $72\div 324=\tfrac29$ and a completely different answer — that is the trap this problem is built around.

3. 3

   Continue left to right with the multiplication.

   $2\cdot 9=18,$

   so the expression is now $49-18-6$.

4. 4

   Perform the additions and subtractions, again left to right.

   $49-18=31,\qquad 31-6=25.$

5. 5

   Check by rewriting as a single fraction. The middle term is $\dfrac{72\cdot 9}{36}=\dfrac{648}{36}=18$, confirming the same value, so

   $7^{2}-72\div 6^{2}\cdot 9-6=25.$