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a
0
=
1
\displaystyle \displaystyle a^{0} = 1
a
0
=
1
a
1
=
a
\displaystyle \displaystyle a^{1} = a
a
1
=
a
a
x
a
y
=
a
x
+
y
\displaystyle \displaystyle a^{x}a^{y} = a^{x+y}
a
x
a
y
=
a
x
+
y
(
a
x
)
y
=
a
x
y
\displaystyle \displaystyle \left(a^{x} \right)^y = a^{xy}
(
a
x
)
y
=
a
x
y
(
a
b
)
x
=
a
x
b
x
\displaystyle \displaystyle \left(ab \right)^x = a^{x}b^{x}
(
a
b
)
x
=
a
x
b
x
a
x
a
y
=
a
x
−
y
\displaystyle \displaystyle \frac{a^{x}}{a^{y}} = a^{x-y}
a
y
a
x
=
a
x
−
y
(
a
b
)
x
=
a
x
b
x
\displaystyle \displaystyle \left( \frac{a}{b} \right)^{x} = \frac{a^{x}}{b^{x}}
(
b
a
)
x
=
b
x
a
x
a
−
n
=
1
a
n
\displaystyle \displaystyle a^{-n} = \frac{1}{a^{n} }
a
−
n
=
a
n
1
a
1
n
=
a
n
\displaystyle \displaystyle a^{ \frac{1}{n} } = \sqrt[n]{a}
a
n
1
=
n
√
a
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