To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{9x^6}{4x^4} \)
\( \frac{9}{4} \) x^{(6 - 4)}
2\(\frac{1}{4}\)x²

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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

3 + (3 + 5) ÷ 2 x 3 - 4²
P: 3 + (8) ÷ 2 x 3 - 4²
E: 3 + 8 ÷ 2 x 3 - 16
MD: 3 + \( \frac{8}{2} \) x 3 - 16
MD: 3 + \( \frac{24}{2} \) - 16
AS: \( \frac{6}{2} \) + \( \frac{24}{2} \) - 16
AS: \( \frac{30}{2} \) - 16
AS: \( \frac{30 - 32}{2} \)
\( \frac{-2}{2} \)
-1

To subtract 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:

\( \frac{6 x 7}{6 x 7} \) - \( \frac{2 x 3}{14 x 3} \)

\( \frac{42}{42} \) - \( \frac{6}{42} \)

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

\( \frac{42 - 6}{42} \) = \( \frac{36}{42} \) = \(\frac{6}{7}\)