The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 32 and 40 have in common.

To simplify a radical, factor out the perfect squares:

\( \sqrt{20} \)
\( \sqrt{4 \times 5} \)
\( \sqrt{2^2 \times 5} \)
2\( \sqrt{5} \)

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{3c^8}{2c^2} \)
\( \frac{3}{2} \) c^{(8 - 2)}
1\(\frac{1}{2}\)c⁶

If 69% of the town's 15,000 voters cast ballots the number of votes cast is:

(\( \frac{69}{100} \)) x 15,000 = \( \frac{1,035,000}{100} \) = 10,350

The mayor got 89% of the votes cast which is:

(\( \frac{89}{100} \)) x 10,350 = \( \frac{921,150}{100} \) = 9,211 votes.

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

7\( \sqrt{80} \) - 9\( \sqrt{5} \)
7\( \sqrt{16 \times 5} \) - 9\( \sqrt{5} \)
7\( \sqrt{4^2 \times 5} \) - 9\( \sqrt{5} \)
(7)(4)\( \sqrt{5} \) - 9\( \sqrt{5} \)
28\( \sqrt{5} \) - 9\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them: