The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

First, solve for \( \left|b + 5\right| \):

\( \left|b + 5\right| \) - 7 = -8
\( \left|b + 5\right| \) = -8 + 7
\( \left|b + 5\right| \) = -1

The value inside the absolute value brackets can be either positive or negative so (b + 5) must equal - 1 or --1 for \( \left|b + 5\right| \) to equal -1:

So, b = -4 or b = -6.

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:

8b⁵ x 8b⁴
(8 x 8)b^{(5 + 4)}
64b⁹

To add these radicals together their radicands must be the same:

6\( \sqrt{175} \) + 6\( \sqrt{7} \)
6\( \sqrt{25 \times 7} \) + 6\( \sqrt{7} \)
6\( \sqrt{5^2 \times 7} \) + 6\( \sqrt{7} \)
(6)(5)\( \sqrt{7} \) + 6\( \sqrt{7} \)
30\( \sqrt{7} \) + 6\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 20 are [1, 2, 4, 5, 10, 20]. They share 3 factors [1, 2, 4] making 4 the greatest factor 36 and 20 have in common.