What Are the Eight Rules of Exponents?
While there are more than eight mathematical rules involving exponents, the Eight Rules of Exponents are a core set of principles which, when properly taught, understood and applied, help students who are new to exponents as they navigate the course of their math education. They are: The Rule of One, The Zero Rule, The Quotient Rule, The Product Rule, The Power Rule, The Negative Rule, The Product to Power Rule and The Quotient to Power Rule.
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The Rule of One and the Zero Rule
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The Rule of One states that for any number x raised to the power of 1, the value is x.
The Zero Rule states that the value of any number x raised to the value of 0 is 1, except when x equals 0.
The Product Rule and the Quotient Rule
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The Product Rule refers to multiplying exponents of the same base, and confers that the product can be expressed by adding together the exponents.
The Quotient Rule, inversely, refers to dividing exponents of the same base and confers that the quotient can be expressed by subtracting the exponent in the denominator from the exponent in the numerator.
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The Power Rule and The Negative Rule
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The Power Rule posits that an exponent raised to an exponent can be expressed by multiplying the exponents together.
The Negative Rule refers to the property by which expressions with negative exponents can be described as the inverse of that expression with a positive exponent, and vice versa.
The Product to Power Rule
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The Product to Power Rule states that any product raised to an exponent is equal to the product of each factor raised to the same exponent.
The Quotient to Power Rule
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The Quotient to Power rule tells us that any quotient taken to an exponent is equal to the numerator taken to that same exponent divided by the denominator taken to said exponent. This does not apply if the denominator is equal to zero.
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References
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Comments
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Birkenheath
Oct 15, 2010
I'm having trouble understanding the last rule, the Quotient to Power Rule. It's hard to see the diagram. Please explain further. Thanks so much!
