In other words, if you raise a nonzero number to the power of
0
,
the result is
1.
Mathematicians debate the value of
0
0
.
Some say it's
1
,
and some say it's undefined.
Here are some examples of the Zero Power Rule. Notice it works for numbers and for variables.
1
0
=
1
(
153
+
x
)
0
=
1
,
if
x
≠
−
153
(
x
+
y
+
z
)
0
=
1
,
if
x
+
y
+
z
≠
0
So when
a
≠
0
,
why does
a
0
=
1
?
Why does the Zero Power Rule hold? Here's one way to think about it:
a
0
=
a
n
−
n
Then, by the quotient rule for exponents, we can write this as:
a
n
−
n
=
a
n
a
n
Then this becomes a problem about dividing fractions. Since the numerator and the denominator are both the same this becomes
1
.
a
n
a
n
=
1
A negative exponent means how many times to divided by the number