Difference between revisions of "Chapter 2: An ancient theorem and a modern question"

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<math> 2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 </math>
<math> 2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 </math>


Multiplying these together we also see that
Multiplying these together we also see that:


<math> 2^3 \cdot 2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 </math>
<math> 2^3 \cdot 2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 2^8</math>


The additive property of exponentiation tells us that
This is known as the additive property of exponentiation. It can be written as:
 
<math> 2^3 \cdot 2^5 = 2^{3+5} <\math>
 
Or more generally:
 
<math> 2^a \cdot 2^b = 2^{a+b} <\math>


== Preliminaries ==
== Preliminaries ==
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