Not all
exponents are positive integers. Some exponents are negative integers. Study
the pattern at the right to find the value of 10–1
and 10–2. Extending
the pattern suggests that 
.
When you multiply
by the base, the exponent in the result increases by one. For example, 103
× 10 = 104.
When you divide by the base, the exponent in the result decreases by one. For
example, 10–2 ÷ 10 = 10–3.
You can use
the Quotient of Powers rule and the definition of power to simplify the
expression 
and write a
definition of negative exponents.
You can
conclude that x–2 and 
are equal because cannot have two
different values. This and other examples suggest the following definition.
1.
Write 10–3 using positive
exponents. Then evaluate the expression.
Alternative Solutions:
To simplify
an expression with a negative exponent, write an equivalent expression that has
positive exponents. Each base should appear only once and all fractions should
be in simplest form.
Example
Simplify
each expression.
Alternative Solutions:
Alternative Solutions:
4. Simplify 
Alternative Solutions:
Biology
Link
5. The E. coli bacteria has a width of 103 millimeter. The head of a pin has a diameter of 1 millimeter. How many E. coli bacteria can fit across the head of a pin?
Alternative Solutions:
To find the number of bacteria,
divide 1 by 10–3.
Since 103 = 1000, about
1000 bacteria could fit across the head of a pin.
Sumber
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