(10*6^n)/(2^(n+1)*3^(n-1))

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To simplify this expression, we can first rewrite the numerator and denominator with the given exponents:

Numerator: 106^n = 10 (2 3)^n = 102^n * 3^n

Denominator: 2^(n+1)3^(n-1) = 2^n 2 3^n 3^(-1) = 23^n 2^n / 3

Now, we can substitute these expressions back into the original expression:

[102^n 3^n] / [23^n 2^n / 3]

Next, we can simplify further by canceling out the common terms:

= (10/2) (3^n/3^n) / (2/3)
= 5 / (2/3)
= 5 3/2
= 15/2 = 7.5

Therefore, (106^n)/(2^(n+1)3^(n-1)) simplifies to 7.5.