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

4\( \sqrt{32} \) - 4\( \sqrt{2} \)
4\( \sqrt{16 \times 2} \) - 4\( \sqrt{2} \)
4\( \sqrt{4^2 \times 2} \) - 4\( \sqrt{2} \)
(4)(4)\( \sqrt{2} \) - 4\( \sqrt{2} \)
16\( \sqrt{2} \) - 4\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{10 + 8 + 10 + 8}{4} \) = \( \frac{36}{4} \) = 9

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{60} \) = \( \frac{\frac{32}{4}}{\frac{60}{4}} \) = \( \frac{8}{15} \)

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.

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:

9x² x 9x²
(9 x 9)x^{(2 + 2)}
81x⁴