To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

8x⁵ - 7x⁵
(8 - 7)x⁵
x⁵

If 67% of the town's 36,000 voters cast ballots the number of votes cast is:

(\( \frac{67}{100} \)) x 36,000 = \( \frac{2,412,000}{100} \) = 24,120

The mayor got 72% of the votes cast which is:

(\( \frac{72}{100} \)) x 24,120 = \( \frac{1,736,640}{100} \) = 17,366 votes.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 2}{6 x 2} \) - \( \frac{5 x 1}{12 x 1} \)

\( \frac{10}{12} \) - \( \frac{5}{12} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{10 - 5}{12} \) = \( \frac{5}{12} \) = \(\frac{5}{12}\)

To simplify a radical, factor out the perfect squares:

\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)

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

3\( \sqrt{63} \) + 4\( \sqrt{7} \)
3\( \sqrt{9 \times 7} \) + 4\( \sqrt{7} \)
3\( \sqrt{3^2 \times 7} \) + 4\( \sqrt{7} \)
(3)(3)\( \sqrt{7} \) + 4\( \sqrt{7} \)
9\( \sqrt{7} \) + 4\( \sqrt{7} \)

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