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This module introduces the concept of exponents in algebra.

An exponent means repeated multiplication. For instance, 10 6 size 12{"10" rSup { size 8{6} } } {} means 10 10 10 10 10 10 size 12{"10" cdot "10" cdot "10" cdot "10" cdot "10" cdot "10"} {} , or 1,000,000.

You’ve probably noticed that there is a logical progression of operations. When you add the same number repeatedly , that’s multiplication. When you multiply the same number repeatedly , that’s an exponent.

However, there is one vital difference: addition and multiplication commute , but exponentiation does not commute . This is a fancy way of saying that order matters. 2 + 3 = 3 + 2 size 12{2+3=3+2} {} ; and 2 3 = 3 2 size 12{2 cdot 3=3 cdot 2} {} , but 2 3 size 12{2 rSup { size 8{3} } } {} is not the same as 3 2 size 12{3 rSup { size 8{2} } } {} .

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Source:  OpenStax, Advanced algebra ii: conceptual explanations. OpenStax CNX. May 04, 2010 Download for free at http://cnx.org/content/col10624/1.15
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