To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{64} \) = \( \frac{\frac{16}{16}}{\frac{64}{16}} \) = \( \frac{1}{4} \)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To add these radicals together their radicands must be the same:

8\( \sqrt{32} \) + 6\( \sqrt{2} \)
8\( \sqrt{16 \times 2} \) + 6\( \sqrt{2} \)
8\( \sqrt{4^2 \times 2} \) + 6\( \sqrt{2} \)
(8)(4)\( \sqrt{2} \) + 6\( \sqrt{2} \)
32\( \sqrt{2} \) + 6\( \sqrt{2} \)

Now that the radicands are identical, you can add them together:

There are 3 3-passenger taxis available so that's 3 x 3 = 9 total seats. There are 11 people needing transportation leaving 11 - 9 = 2 who will have to find other transportation.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%