If 79% of the town's 10,000 voters cast ballots the number of votes cast is:

(\( \frac{79}{100} \)) x 10,000 = \( \frac{790,000}{100} \) = 7,900

The mayor got 58% of the votes cast which is:

(\( \frac{58}{100} \)) x 7,900 = \( \frac{458,200}{100} \) = 4,582 votes.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

7,235,000 in scientific notation is 7.235 x 10⁶

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{7 x 2}{2 x 2} \) - \( \frac{3 x 1}{4 x 1} \)

\( \frac{14}{4} \) - \( \frac{3}{4} \)

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

\( \frac{14 - 3}{4} \) = \( \frac{11}{4} \) = 2\(\frac{3}{4}\)

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:

-6y⁶ x 3y⁴
(-6 x 3)y^{(6 + 4)}
-18y¹⁰