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## Answers

10500 = 3 × 2 × 1750

10500 = 3 × 2 × 2 × 875

10500 = 3 × 2 × 2 × 5 × 175

10500 = 3 × 2 × 2 × 5 × 5 × 35

10500 = 2 × 2 × 3 × 5 × 5 × 5 × 7

Here we see that 2³ × 3 × 5³ × 7 = 2 × 2 × 3 × 5 × 5 × 5 × 7

Now it's simple.

The first factor is 2, and in the equation 2 is raised to m. There are two 2s in the factorization. Therefore m=2.

Then 3 is present in both. 5 is then raised to n. 5 comes 3 times. Therefore n=3.

Then the 7 appears in both equations.

**Ans: m=2 and n=3**