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:

\( \sqrt{\frac{64}{25}} \)
\( \frac{\sqrt{64}}{\sqrt{25}} \)
\( \frac{\sqrt{8^2}}{\sqrt{5^2}} \)
\( \frac{8}{5} \)
1\(\frac{3}{5}\)

If 73% of the town's 24,000 voters cast ballots the number of votes cast is:

(\( \frac{73}{100} \)) x 24,000 = \( \frac{1,752,000}{100} \) = 17,520

The mayor got 71% of the votes cast which is:

(\( \frac{71}{100} \)) x 17,520 = \( \frac{1,243,920}{100} \) = 12,439 votes.

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

45% of the water consumption is industrial use and 29% is personal use so (45% - 29%) = 16% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{16}{100} \) x 30,000 gallons = 4,800 gallons.

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:

\( \frac{-7z^5}{3z^2} \)
\( \frac{-7}{3} \) z^{(5 - 2)}
-2\(\frac{1}{3}\)z³