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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:

\( \frac{2y^7}{6y^2} \)
\( \frac{2}{6} \) y^{(7 - 2)}
\(\frac{1}{3}\)y⁵

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

3 + (2 + 2) ÷ 4 x 2 - 2²
P: 3 + (4) ÷ 4 x 2 - 2²
E: 3 + 4 ÷ 4 x 2 - 4
MD: 3 + \( \frac{4}{4} \) x 2 - 4
MD: 3 + \( \frac{8}{4} \) - 4
AS: \( \frac{12}{4} \) + \( \frac{8}{4} \) - 4
AS: \( \frac{20}{4} \) - 4
AS: \( \frac{20 - 16}{4} \)
\( \frac{4}{4} \)
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To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{5} \) x \( \frac{2}{5} \) = \( \frac{2 x 2}{5 x 5} \) = \( \frac{4}{25} \) = \(\frac{4}{25}\)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

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

\( \frac{8 x 3}{8 x 3} \) + \( \frac{8 x 2}{12 x 2} \)

\( \frac{24}{24} \) + \( \frac{16}{24} \)

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

\( \frac{24 + 16}{24} \) = \( \frac{40}{24} \) = 1\(\frac{2}{3}\)