Please Excuse My Dear Aunt Sally (PEMDAS), she has the hardest time remembering how to make sense of these arithmetic rules...

\[ \large \color{red}3^{\color{blue}{1506}} - \color{red}3^{\color{blue}{1505}} = \ ? \]

Evaluate \[ \left( 20142014 \times 20142014-20142004 \times 20142024 \right).\]

\[\Large \color{blue}{n}^{\color{red}{200}} < \color{green}{5}^{\color{brown}{300}}\]

Find the largest integer \(n\) that satisfies the above inequality.

What is the sum of the sums of numbers on the 2 diagonals?

**Note that the center square is added twice.**

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