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Laws of Exponents



Here are the "Laws of Exponents" or rules that our Exponent Calculator uses to calculate your answer. For illustration, we use b for bases, and n for exponents.

bn means b multiplied by itself n times. For example, 34 is 3 x 3 x 3 x 3 = 81. However, there are certain exceptions and rules that our Exponent Calculator follows. Here are those rules with examples:



Rule 1: Powers of one.

b1=b

01=0

11=1

1231=123



Rule 2: Powers of zero

10=1

1230=1



Rule 3: Powers of minus one

b-1=1b

123-1=1123= 0.00813



Rule 4: Negative Exponents

b-n=1bn

12-3=1123= 0.00058

      
      



Conflicting Laws

If the base is 0 and the exponent is 0, then Rule 1 and Rule 2 conflict.

According to Rule 1 the answer should be 0 and according to Rule 2 the answer should be 1.

You can't have it both ways. Therefore, we consider this problem "undefined".

00=undefined




Answer too long

If your answer is too large or too small to display on your screen, you will get "Answer too Long" as the answer using our Exponent Calculator.




Almost 0

If your answer is too large or too small to display on your screen, you will get "Answer too Long" as the answer using our Exponent Calculator.



 


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