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

\( \frac{14 + 6 + 11 + 9}{4} \) = \( \frac{40}{4} \) = 10

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{8 x 3}{3 x 3} \) - \( \frac{6 x 1}{9 x 1} \)

\( \frac{24}{9} \) - \( \frac{6}{9} \)

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

\( \frac{24 - 6}{9} \) = \( \frac{18}{9} \) = 2

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-1x⁶ + 6x⁶
(-1 + 6)x⁶
5x⁶

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

7\( \sqrt{50} \) + 4\( \sqrt{2} \)
7\( \sqrt{25 \times 2} \) + 4\( \sqrt{2} \)
7\( \sqrt{5^2 \times 2} \) + 4\( \sqrt{2} \)
(7)(5)\( \sqrt{2} \) + 4\( \sqrt{2} \)
35\( \sqrt{2} \) + 4\( \sqrt{2} \)

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

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:

6b⁷ x 7b⁶
(6 x 7)b^{(7 + 6)}
42b¹³