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You decide the order

Xanathar's Guide to Everything, pg. 77 gives guidance on adjudicating situations when things are happening simultaneously:

###Simultaneous Effects

Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature’s turn. If two or more things happen at the same time on a character or monster’s turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character’s turn, the player decides which of the two effects happens first.

It gives the player whose turn it is advantage, and ensures more fun, because it favors the current player.

You decide the order

Xanathar's Guide to Everything, pg. 77 gives guidance on adjudicating situations when things are happening simultaneously:

Simultaneous Effects

Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature’s turn. If two or more things happen at the same time on a character or monster’s turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character’s turn, the player decides which of the two effects happens first.

It gives the player whose turn it is advantage, and ensures more fun, because it favors the current player.

You decide the order

Xanathar's Guide to Everything, pg. 77 gives a guidance when things happening simultaneously

Simultaneous Effect
Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table-whether player or DM-who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character's turn, the player decides which of the two effects happens first.

It gives the player whose turn at play advantage, and ensures more fun, because it favors the current player.

You decide the order

Xanathar's Guide to Everything, pg. 77 gives guidance on adjudicating situations when things are happening simultaneously:

###Simultaneous Effects

Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature’s turn. If two or more things happen at the same time on a character or monster’s turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character’s turn, the player decides which of the two effects happens first.

It gives the player whose turn it is advantage, and ensures more fun, because it favors the current player.

D&D resolves things sequentially

When you do multiple things to a target, like two attacks, or cast two spells (action and bonus action spell), you choose the order of the actions, except when the description says otherwise.

Example: if you cast misty step and shocking grasp, you can choose the order of the action. You can cast misty step to get in range of your target, then cast shocking grasp. Or you can cast shocking grasp first, then misty step away without provoking opportunity attack.

Example of exception: Shield Master says if you take Attack action, you can do as a bonus action ..., means you must take Attack action first and resolve it, before being able to use your bonus action to shove the enemy.

Attacks are resolved individually, meaning one attack and anything triggered from the attack is resolved separately, then after that the other attack is resolved.

In your example, if one of your attack cause the target to become prone, and another explodes (Bursting Arrow), after you choose the order of attack (prone -> explode), you resolve them separately.

1. Apply damage, then target become prone, and immediately fall up to 500 ft per turn.
2. Bursting Arrow now deals area of effect damage around on where they landed.

Note that you can declare each attack after the other resolve, meaning seeing the first target has fallen down and now is out of reach, you can choose another target.

You can also use Bursting Arrow first, then knocking them prone, if you want.

You decide the order

Xanathar's Guide to Everything, pg. 77 gives a guidance when things happening simultaneously

Simultaneous Effect
Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table-whether player or DM-who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character's turn, the player decides which of the two effects happens first.

It gives the player whose turn at play advantage, and ensures more fun, because it favors the current player.