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Let's quickly review how an exponent works...
An exponent is a number which tells us how many times to
multiply a factor (either a numerical, or a variable
factor) times itself. This
"factor" is called the
base.
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For example: in 54, which is read:
"five to the
fourth power"
The
base is 5
and the exponent
is 4.
In this example x5, which is read:
"x to the fifth power"
The base is x and the exponent is 5 |
Using the rule stated above the result would be
*for a numerical base;
54 = 5•5•5•5=625
*for a variable base;
x5 = x•x•x•x•x
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Now let's look at the special rule for exponents under the
operation of multiplication. |
We know that 32
means 3•3 and 33 means 3•3•3
therefore 32•33 = 3•3•3•3•3
or 35
using a variable factor
a4•a2 = a•a•a•a•a•a
or a6
If you look closely you'll see that the exponent in
the product is equal to the sum of the exponents in each of
the factors.
In general the rule of exponents, when multiplying
powers of the same base, is:
xa •xb = x a+b
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*Note: This rule does
NOT work if the bases
are NOT the same.
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22•33 cannot be simplified
using the rule of exponents stated above because;
22•33 = 2•2•3•3•3
and not all of the factors (bases) are the same.
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