1.

Suppose ‘m’ and ‘n’ are distinct integers \(\frac{3^m \times2^n}{2^m\times3^n}\) can be an integer? Give reasons.

Answer»

\(\frac{3^m \times2^n}{2^m\times3^n}\) = \(\frac{3^{m - n}}{2^{m - n}}\)

If ‘m’ and ‘n’ are two distinct integers. 

Then 3(m-n) is always on odd number and 2(m-n) is always an even number. If odd number is divided, by an even number the quotient is not an integer. 

Therefore it is’not an integer.



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