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:

6x⁶ + 4x⁶
(6 + 4)x⁶
10x⁶

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{9} \) ÷ \( \frac{1}{5} \) = \( \frac{1}{9} \) x \( \frac{5}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{9} \) x \( \frac{5}{1} \) = \( \frac{1 x 5}{9 x 1} \) = \( \frac{5}{9} \) = \(\frac{5}{9}\)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

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

\( \frac{4 x 2}{6 x 2} \) + \( \frac{3 x 1}{12 x 1} \)

\( \frac{8}{12} \) + \( \frac{3}{12} \)

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

\( \frac{8 + 3}{12} \) = \( \frac{11}{12} \) = \(\frac{11}{12}\)

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

4 + (4 + 5) ÷ 5 x 3 - 3²
P: 4 + (9) ÷ 5 x 3 - 3²
E: 4 + 9 ÷ 5 x 3 - 9
MD: 4 + \( \frac{9}{5} \) x 3 - 9
MD: 4 + \( \frac{27}{5} \) - 9
AS: \( \frac{20}{5} \) + \( \frac{27}{5} \) - 9
AS: \( \frac{47}{5} \) - 9
AS: \( \frac{47 - 45}{5} \)
\( \frac{2}{5} \)
\(\frac{2}{5}\)