Question

Suppose m and n are distinct integers. Can $\frac{3^m \times 2^n}{2^m \times 3^n}$ be an integer? Give reasons.

Answer 1

False .

Explanation:

( 3^m × 2ⁿ )/( 2^m × 3ⁿ )

If m = 2 , n = 3

[ m, n are distinct integers ]

= ( 3² × 2³ )/( 2² × 3³ )

= ( 2^3-2 )/( 3^3-2 )

= 2/3 is not an integer

Therefore ,

If m, n are distinct integers ,

( 3^m × 2ⁿ )/( 2^m × 3ⁿ ) is not an

integer.

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