Power Countdown

In the game of Power Countdown, you use a set of numbers to make a target number. The only operation you can use is raising something to a power, but you are allowed to use fractional powers - you can use a $3$ to raise a number to the power $3$ or $1\over3$.

Each number can only be used once.You don't have to use all the numbers!

Here is an example:



One way of making the target is:



Can you find any other ways of making $8$?
Are there any ways which use all the numbers?

Here is another selection.


How many ways are there to make the target number of $125$?


Below is a selection of numbers and five targets.



How many different ways can you find to make each target?

Are there any targets you can't make? How close can you get?