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

7\( \sqrt{5} \) x 8\( \sqrt{6} \)
(7 x 8)\( \sqrt{5 \times 6} \)
56\( \sqrt{30} \)

The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 have in common.

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):

2 + (3 + 3) ÷ 5 x 2 - 5²
P: 2 + (6) ÷ 5 x 2 - 5²
E: 2 + 6 ÷ 5 x 2 - 25
MD: 2 + \( \frac{6}{5} \) x 2 - 25
MD: 2 + \( \frac{12}{5} \) - 25
AS: \( \frac{10}{5} \) + \( \frac{12}{5} \) - 25
AS: \( \frac{22}{5} \) - 25
AS: \( \frac{22 - 125}{5} \)
\( \frac{-103}{5} \)
-20\(\frac{3}{5}\)

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:

-3c³ x 2c⁴
(-3 x 2)c^{(3 + 4)}
-6c⁷