Question

What is six with the power of 9/6 to the power of five is the answer six power of four or six power of 14 or six power of 1.8 or just six which one is the answer

Answer 1

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 \( 6^{6.5} \).