{"id":584,"date":"2024-04-23T01:32:31","date_gmt":"2024-04-23T01:32:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&p=584"},"modified":"2024-11-20T00:52:47","modified_gmt":"2024-11-20T00:52:47","slug":"exponents-and-scientific-notation-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/exponents-and-scientific-notation-learn-it-4\/","title":{"raw":"Exponents and Scientific Notation: Learn It 4","rendered":"Exponents and Scientific Notation: Learn It 4"},"content":{"raw":"

The Zero Exponent Rule<\/h2>\r\nThe Zero Exponent Rule is a somewhat counterintuitive yet fundamental rule in mathematics. It tells us that any nonzero number raised to the power of zero is equal to one. This might seem strange at first because multiplying a number by itself zero times is an abstract concept. However, this rule is consistent with the patterns observed when decreasing the exponent by one and dividing by the base each time.\r\n\r\nThe rule that any number to the power of one is the number itself reinforces the identity property of exponentiation. It is crucial to understand these rules thoroughly as they form the basis for more complex operations in algebra, calculus, and beyond.\r\n\r\n
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exponents of [latex]0[\/latex] or [latex]1[\/latex]<\/h3>\r\nAny number or variable raised to a power of [latex]1[\/latex] is the number itself.\r\n\r\n \r\n

[latex]n^{1}=n[\/latex]<\/p>\r\n \r\n\r\nAny non-zero number or variable raised to a power of [latex]0[\/latex] is equal to [latex]1[\/latex]\r\n\r\n \r\n

[latex]n^{0}=1[\/latex]<\/p>\r\n \r\n\r\nThe quantity [latex]0^{0}[\/latex]\u00a0is undefined.\r\n\r\n<\/div>\r\n<\/section>

[ohm2_question hide_question_numbers=1]6864[\/ohm2_question]<\/section>\r\n

The Negative Exponent Rule<\/h2>\r\nThe Negative Exponent Rule is another vital concept in mathematics, particularly when working with powers and roots. This rule tells us that any nonzero number raised to a negative exponent is equal to the [pb_glossary id=\"13459\"]reciprocal [\/pb_glossary] of that number raised to the corresponding positive exponent. It's a way of expressing division as an exponentiation operation, and it's particularly useful when simplifying expressions that involve division of variables with exponents.\r\n\r\n
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the negative rule of exponents<\/h3>\r\nWith [latex]a[\/latex], [latex]b[\/latex], [latex]m[\/latex], and [latex]n[\/latex] not equal to zero, and [latex]m[\/latex] and [latex]n[\/latex] as integers, the following rules apply:\r\n

[latex]a^{-m}=\\frac{1}{a^{m}}[\/latex]<\/p>\r\n \r\n

[latex]\\frac{1}{a^{-m}}=a^{m}[\/latex]<\/p>\r\n \r\n

[latex]\\frac{a^{-n}}{b^{-m}}=\\frac{b^m}{a^n}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/section>

[ohm2_question hide_question_numbers=1]6892[\/ohm2_question]<\/section>","rendered":"

The Zero Exponent Rule<\/h2>\n

The Zero Exponent Rule is a somewhat counterintuitive yet fundamental rule in mathematics. It tells us that any nonzero number raised to the power of zero is equal to one. This might seem strange at first because multiplying a number by itself zero times is an abstract concept. However, this rule is consistent with the patterns observed when decreasing the exponent by one and dividing by the base each time.<\/p>\n

The rule that any number to the power of one is the number itself reinforces the identity property of exponentiation. It is crucial to understand these rules thoroughly as they form the basis for more complex operations in algebra, calculus, and beyond.<\/p>\n

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exponents of [latex]0[\/latex] or [latex]1[\/latex]<\/h3>\n

Any number or variable raised to a power of [latex]1[\/latex] is the number itself.<\/p>\n

 <\/p>\n

[latex]n^{1}=n[\/latex]<\/p>\n

 <\/p>\n

Any non-zero number or variable raised to a power of [latex]0[\/latex] is equal to [latex]1[\/latex]<\/p>\n

 <\/p>\n

[latex]n^{0}=1[\/latex]<\/p>\n

 <\/p>\n

The quantity [latex]0^{0}[\/latex]\u00a0is undefined.<\/p>\n<\/div>\n<\/section>\n