To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

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

\( \frac{7 x 7}{6 x 7} \) + \( \frac{3 x 3}{14 x 3} \)

\( \frac{49}{42} \) + \( \frac{9}{42} \)

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

\( \frac{49 + 9}{42} \) = \( \frac{58}{42} \) = 1\(\frac{8}{21}\)

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

4 + (5 + 4) ÷ 5 x 2 - 5²
P: 4 + (9) ÷ 5 x 2 - 5²
E: 4 + 9 ÷ 5 x 2 - 25
MD: 4 + \( \frac{9}{5} \) x 2 - 25
MD: 4 + \( \frac{18}{5} \) - 25
AS: \( \frac{20}{5} \) + \( \frac{18}{5} \) - 25
AS: \( \frac{38}{5} \) - 25
AS: \( \frac{38 - 125}{5} \)
\( \frac{-87}{5} \)
-17\(\frac{2}{5}\)

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

4\( \sqrt{8} \) x 8\( \sqrt{6} \)
(4 x 8)\( \sqrt{8 \times 6} \)
32\( \sqrt{48} \)

Now we need to simplify the radical:

32\( \sqrt{48} \)
32\( \sqrt{3 \times 16} \)
32\( \sqrt{3 \times 4^2} \)
(32)(4)\( \sqrt{3} \)
128\( \sqrt{3} \)

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:

-5z² + 7z²
(-5 + 7)z²
2z²

The factors of a number are all positive integers that divide evenly into the number. The factors of 64 are 1, 2, 4, 8, 16, 32, 64.