Exponents are also referred to as "powers".
For example, 2^{3} can be
read as "two cubed" or as
"two raised to the third power".
Exponents of Negative Values 
When
we multiply negative numbers together, we
must
utilize parentheses to switch to exponent notation.
(3)(3)(3)(3)(3)(3) =
(3)^{6}
BEWARE!!
3^{6}
is NOT the same as
(3)^{6}
The missing parentheses mean that 3^{6}
will multiply
six
3's together
first (by order of operations), and then
take
the negative of that answer.
(3)^{6}
= 729
but
3^{6}
= 729
so be
careful with negative values and exponents !
Note:
Even powers of negative
numbers allow for the negative values to be arranged
in pairs. This pairing guarantees that the answer will
always be positive.
(5)^{6} 
=
(5)•(5) • (5)•(5)
• (5)•(5)
← All pairs. 

= 25
• 25
• 25 

= 15625
(a positive answer) 
Odd powers
of negative numbers, however,
always leave one factor of the negative number not paired.
This one lone negative term guarantees that the answer will
always be negative.
(5)^{5} 
=
(5)•(5) • (5)•(5)
• (5) ←One
lone, unpaired, negative. 

= 25
• 25
• (5) 

= 3125
(a negative answer) 
