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

8\( \sqrt{4} \) x 7\( \sqrt{7} \)
(8 x 7)\( \sqrt{4 \times 7} \)
56\( \sqrt{28} \)

Now we need to simplify the radical:

56\( \sqrt{28} \)
56\( \sqrt{7 \times 4} \)
56\( \sqrt{7 \times 2^2} \)
(56)(2)\( \sqrt{7} \)
112\( \sqrt{7} \)

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.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (3 + 4) ÷ 3 x 2 - 4²
P: 5 + (7) ÷ 3 x 2 - 4²
E: 5 + 7 ÷ 3 x 2 - 16
MD: 5 + \( \frac{7}{3} \) x 2 - 16
MD: 5 + \( \frac{14}{3} \) - 16
AS: \( \frac{15}{3} \) + \( \frac{14}{3} \) - 16
AS: \( \frac{29}{3} \) - 16
AS: \( \frac{29 - 48}{3} \)
\( \frac{-19}{3} \)
-6\(\frac{1}{3}\)

The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 24 and 56 have in common.

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:

-8z³ x 7z⁵
(-8 x 7)z^{(3 + 5)}
-56z⁸