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:

-8b⁶ x 5b⁶
(-8 x 5)b^{(6 + 6)}
-40b¹²

1

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

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

\( \frac{4 x 2}{8 x 2} \) - \( \frac{6 x 1}{16 x 1} \)

\( \frac{8}{16} \) - \( \frac{6}{16} \)

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

\( \frac{8 - 6}{16} \) = \( \frac{2}{16} \) = \(\frac{1}{8}\)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{10\sqrt{10}}{5\sqrt{2}} \)
\( \frac{10}{5} \) \( \sqrt{\frac{10}{2}} \)
2 \( \sqrt{5} \)

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).