The number 1 has several important properties that are useful in algebra. Table 1 gives these properties.
|Multiplication by 1||Anything times one equals itself.||a · 1 = 1 · a = a||Property of Multiplication by 1|
|Division by 1||Anything divided by one remains unchanged.||a / 1 = a||Property of Division by 1|
|Exponent of 1||Any number raised to the power of 1 equals itself.||a1 = a||none|
|Idempotence||1 is idempotent under multiplication and exponentiation.||1 · 1 = 1, 11 = 1||Idempotence|
|Table 1: Properties of one.|
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