Power of a Quotient Property
[Quotient of Powers (Common Exponent)]
Initial Definition

If "a" and "b" are non-zero integer and "m" is a whole number, then:

Quotient of Powers (Common Exponent) Property

When dividing powers with a common exponent, the result can be found by dividing the bases and retaining the exponent.



By the symmetric property of equality, this property can be written either way.

Quotient of Powers (Common Base) Property

Usually it is written as shown below and is called the "power of a quotient" property.

Power of a Quotient Property

Explanation        Quotient of Powers (Common Exponent)
Quotient of Powers (Common Base) Property

Notice that the exponents are all the same (one).


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Quotient of Powers (Common Base) Property
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Quotient of Powers (Common Base) Property
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Generalization

Quotient of Powers (Common Exponent) Property

Explanation        Power of a Quotient Property
Quotient of Powers (Common Base) Property
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Generalization

Power of a Quotient Property