The answer really depends on what number you are doubling.
Let's say that you wish to double the number a (which we assume is greater than 0).
If we're raising a to the nth power, then n must satisfy the following equation:
an = 2a
Taking the natural log on both sides,
n log a = log (2a),
n = log (2a) / log a.
So if we double the number a, it is raised to the log (2a) / log a power.
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The power could then be called an exponent. The number that is being raised to a power is called the base. In the case of 42, the exponent is 2 and the base is 4.
A number raised to the second power is a number times itself. This can also be stated as a number squared.
5 raised to the 3rd power is 125.
If a number raised to the second power is squared and raised to the third power is cubed, I'm going to take a guess and say that a number raised to the fourth power is tesseracted.
a cubed number or a number to the third power