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.
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.