Dividing with Exponents
⇒ Definition of Negative Exponent
Note:
They are reciprocals.
Example 1:
a)
Notice that a negative exponent does not affect the sign of
the number.
b)

→ Odd or Even exponents determine the sign. 
c)

d)
⇒ Division of powers with positive exponents:
Notice that 7 − 3 = 4.
or 

Subtract the smaller exponent from the
larger exponent and put the resulting "power"
in the "place" of the larger "power".
Put a 1 in the numerator if the larger "power" is in the denominator.

Example 2:
→ Notice that 7 â€“ 3 = 7 + (3) = + 4
⇒ Operation of powers with negative exponents: Two methods:
Method 1: Follow the rule above carefully keeping the negative exponents in parens:
Example 3:
a)
Since 7 > 2 work in the numerator:
b)
Since 2 > 8 work in the denominator:
c)
Since  4 >  9 work in the denominator:
Method 2: To multiply or divide with "most" negative exponents, multiply both the numerator and the
denominator by the "reciprocal with positive power" and "neutralize the negative".
Example 4:
a)
Since  2 is
"most negative" multiply both by
b)
Since  8
"most negative" multiply both by
c)
Since  9 is
"most negative" multiply both by
d)
Since  7 < 3, or  7 is
"most negative" multiply by x^{7} ⇒
or
NOTE: Where there are several terms in the numerator and several terms in the
denominator
separate them into a product of fractions with "same letters"
Definition of Zero Exponent a^{ 0 }= 1
Note: The result of raising any base to the 0 exponent
will always be 1. (a ≠ 0)
Example 5:
1. (57x^{ 9} y^{ 32} z^{ 25} )^{0} = 1
2.
