Final answer:
After analyzing each pair of fractions, the only equivalent pair is -1a²b/2 (4) with 5a^4b/-10a² (b). Thus, the correct answer to match the pairs of equivalent fractions is option b: 1, 2, and 4.
Step-by-step explanation:
The question asks us to match pairs of equivalent fractions. Equivalent fractions are different expressions of the same number, often achieved by multiplying or dividing both the numerator and the denominator by the same number or by utilizing properties of exponents. To determine equivalency, we simplify or manipulate both fractions to see if they can be transformed into the same form.
- For 3a/b² and 4a/8ab, by simplifying 4a/8ab we divide both sides of the fraction by 4a, resulting in 1/2b, which is not equivalent to 3a/b². Thus, they are not a match.
- 3b²/1a² and 9b³/-3a²b, by dividing 9b³ by -3a²b we get -3b²/a², which is the negative reciprocal of 3b²/a². They are not equivalent, so they do not match.
- -1/2b and 3a^4/1a³b², these fractions have different variables and exponents so they cannot be equivalent.
- -1a²b/2 and 5a^4b/-10a², we can simplify the second fraction to -a²b/2, which is equivalent to the first. Therefore, these two fractions match.
According to the above analysis, the only equivalent pair is 4 (-1a²b/2) with b (5a^4b/-10a²), so the correct answer is 1,2 and 4 (option b).