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:

\( \frac{-5z^7}{4z^3} \)
\( \frac{-5}{4} \) z^{(7 - 3)}
-1\(\frac{1}{4}\)z⁴

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{4 x 5}{6 x 5} \) - \( \frac{3 x 3}{10 x 3} \)

\( \frac{20}{30} \) - \( \frac{9}{30} \)

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

\( \frac{20 - 9}{30} \) = \( \frac{11}{30} \) = \(\frac{11}{30}\)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{5 \text{ gallons}}{1 \text{ gallons}} \) = 5

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).