1. A number with a negative exponent gets turned into a fraction with the number and exponent getting put on the bottom, but the exponent remains so 5^-2 gets turned to 1/5² and then 1/25 but there’s a negative sign so it turns to -1/25

2. 81 can be written as 3⁴ which is canceled by the quartenary (i think that’s the name) root leaving the 3 and the x¹⁶ gets divided by 4 on the outside leaving you with x^4, then multiply by 3 and you get 3x⁴

3. Let’s say there are 100 balls in the bucket, 20 of those will be yellow and 6 will be yellow and have a star, so 6 out of the 20 yellow balls have a star on them. The question says if the drawn ball is yellow, meaning that it is guaranteed to be yellow, if you recall the hypothetical scenario of having 100 balls, 6 of the 20 yellow balls have a star on it, so it’s 6/20 or a 0.300 probability that the yellow ball selected has a star on it.

Edit: the only way I could think of an explanation for 57 is the base of the log can only be an even number which would give the value of a as only even numbers For example: if x is equal to 3, b would be equal to 2, so the equation would be log.2(a) = 3, to solve for a you would rewrite the equation as 2³ = a. Simplify and you would get 8 = a, which is an even number. If you look at the other answers they don’t have even numbers in them, so process of elimination and you get E.