Solution: 40 to the Power of 12 is equal to 16777216000000000000
Methods
Step-by-step: finding 40 to the power of 12
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:
4
0
12
40^{12}
4 0 12
To simplify this, all that is needed is to multiply it out:
40 x 40 x 40 x 40 x ... (for a total of 12 times) = 16777216000000000000
Therefore, 40 to the power of 12 is 16777216000000000000.
Related exponent problems:
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