To solve the expression \( 6^{\frac{9}{6}} \times 6^5 \), you can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
Starting with your expression:
\[ 6^{\frac{9}{6}} \times 6^5 = 6^{\left(\frac{9}{6} + 5\right)} \]
Next, convert \( 5 \) into a fraction with a denominator of 6:
\[ 5 = \frac{30}{6} \]
Now, add the two fractions:
\[ \frac{9}{6} + \frac{30}{6} = \frac{9 + 30}{6} = \frac{39}{6} \]
Now we simplify \( \frac{39}{6} \):
\[ \frac{39}{6} = \frac{13}{2} = 6^{\frac{13}{2}} \]
Thus, \( 6^{\frac{9}{6}} \times 6^5 = 6^{\frac{39}{6}} \).
Now we compare \( 6^{\frac{39}{6}} \) to the options you provided: \( 6^4, 6^{14}, 6^{1.8}, \) and \( 6 \).
Since \( \frac{39}{6} = 6.5 \), this does not match any of your options directly.
In numerical form, \( 6^{6.5} \) is significantly greater than any of the choices provided.
However, to align it with your options, it's valuable to note that \( 39/6 \approx 6.5 \). None of the options exactly match this estimate.
So, the original question has no correct answers among the options provided; the exact result is \( 6^{6.5} \).