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:

\( \frac{z^9}{5z^2} \)
\( \frac{1}{5} \) z^{(9 - 2)}
\(\frac{1}{5}\)z⁷

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{36}{81}} \)
\( \frac{\sqrt{36}}{\sqrt{81}} \)
\( \frac{\sqrt{6^2}}{\sqrt{9^2}} \)
\(\frac{2}{3}\)

The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 have in common.

If 43% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{43}{100} \)) x 44,000 = \( \frac{1,892,000}{100} \) = 18,920

The mayor got 86% of the votes cast which is:

(\( \frac{86}{100} \)) x 18,920 = \( \frac{1,627,120}{100} \) = 16,271 votes.

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.