Solution: 21 to the Power of 100 is equal to 1.6669764843963375e+132
Methods
Step-by-step: finding 21 to the power of 100
The first step is to understand what it means when a number has an exponent. The “power” of a number indicates how many times the base would be multiplied by itself to reach the correct value.
The second step is to write the number in the base-exponent form, and lastly calculate what the final result would be. Consider the example of 2 to the power of 4: in exponent form that would be
2
4
2^4
2 4
. To solve this, we need to multiply the base, 2 by itself, 4 times -
2
⋅
2
⋅
2
⋅
2
2\cdot2\cdot2\cdot2
2 ⋅ 2 ⋅ 2 ⋅ 2
= 16. So
2
4
=
16
2^4 = 16
2 4 = 16
.
So re-applying these steps to our particular problem, we first convert our word problem to a base-exponent form of:
2
1
100
21^{100}
2 1 100
To simplify this, all that is needed is to multiply it out:
21 x 21 x 21 x 21 x ... (for a total of 100 times) = 1.6669764843963375e+132
Therefore, 21 to the power of 100 is 1.6669764843963375e+132.
Related exponent problems:
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