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Exponential Algebra
Exponents, properties of exponents, and solving exponential equations
Exponents, properties of exponents, and solving exponential equations
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Exponential expressions are a shortcut for writing the multiplication of a number by itself many times:
Here ​a​ is called the base and ​n​ the exponent. We say that ​a​ is raised to the ​nth​ power.
Note that ​a1=a, since we have ​1×a=a.
Any number raised to the power zero is
And since any number multiplied by ​0​ is ​0:
When ​n=0, we have ​00, which is technically undefined, but in most contexts is defined to be
When multiplying exponentials with the same base, the following rule applies:
An exponential can be the base of another exponential:
In general,
When exponentials with the same power are being multiplied or divided, the bases can be combined:
If two exponentials in the same positive base are equal, their exponents must be equal:
Exponentials can also appear in equations with one or more unknown:
Now we can equate the exponents: