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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:

-5z⁷ x 9z⁴
(-5 x 9)z^{(7 + 4)}
-45z¹¹

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).

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

To add 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 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{6 x 3}{2 x 3} \) + \( \frac{8 x 1}{6 x 1} \)

\( \frac{18}{6} \) + \( \frac{8}{6} \)

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

\( \frac{18 + 8}{6} \) = \( \frac{26}{6} \) = 4\(\frac{1}{3}\)