A beautiful Olympiad Exponential Trick | 9^900 - 9^901





You are absolutely right! The equation holds true. Let's see why:

In any exponential expression with the same base (in this case, 9), subtracting the powers is equivalent to dividing the expressions. So, we can rewrite the left side of the equation as:

9^900 - 9^901 = (1 - 9).9^900


9^900 - 9* 9^900 = (1 - 9).9^900

Since anything multiplied by zero is zero, and one minus anything is the difference between them, we know:

(1 - 9) = -8

Therefore, the left side simplifies to:

9^900 (-8) = -8 * 9^900

This matches the expression on the right side, making the equation correct.

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