The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

If 87% of the town's 14,000 voters cast ballots the number of votes cast is:

(\( \frac{87}{100} \)) x 14,000 = \( \frac{1,218,000}{100} \) = 12,180

The mayor got 67% of the votes cast which is:

(\( \frac{67}{100} \)) x 12,180 = \( \frac{816,060}{100} \) = 8,161 votes.

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:

\( \frac{7b^7}{6b^3} \)
\( \frac{7}{6} \) b^{(7 - 3)}
1\(\frac{1}{6}\)b⁴

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:

\( \sqrt{\frac{16}{9}} \)
\( \frac{\sqrt{16}}{\sqrt{9}} \)
\( \frac{\sqrt{4^2}}{\sqrt{3^2}} \)
\( \frac{4}{3} \)
1\(\frac{1}{3}\)

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

-y⁵ x 4y²
(-1 x 4)y^{(5 + 2)}
-4y⁷