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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: