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Powers and roots
Powers and roots
7 formulas · Mathematics
Product of powers with the same base
a
m
⋅
a
n
=
a
m
+
n
a^m\cdot a^n=a^{m+n}
a
m
⋅
a
n
=
a
m
+
n
Quotient of powers
a
m
a
n
=
a
m
−
n
\dfrac{a^m}{a^n}=a^{m-n}
a
n
a
m
=
a
m
−
n
Power of a power
(
a
m
)
n
=
a
m
n
(a^m)^n=a^{mn}
(
a
m
)
n
=
a
mn
Power of a product
(
a
b
)
n
=
a
n
b
n
(ab)^n=a^n b^n
(
ab
)
n
=
a
n
b
n
Power with a negative exponent
a
−
n
=
1
a
n
a^{-n}=\dfrac{1}{a^n}
a
−
n
=
a
n
1
Root as a fractional power
a
m
n
=
a
m
/
n
\sqrt[n]{a^m}=a^{m/n}
n
a
m
=
a
m
/
n
Root of a product
a
b
n
=
a
n
b
n
\sqrt[n]{ab}=\sqrt[n]{a}\,\sqrt[n]{b}
n
ab
=
n
a
n
b
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