Exponent Rules
Product Rule
If
0, and
and
Quotient Rule
are real numbers, then
If
·
0, and
and
are real numbers, then
Multiplying with same base, keep the base and add
the exponents
·
Ex:
Dividing with same base, keep the base and
subtract the exponents
Ex:
Power‐to‐Power Rule
If
0, and
and
are real numbers, then
·
Quotient‐to‐Power Rule
A base to a power, to another power, keep the
base and multiply the exponents
0, and
is a real number, then
Quotient to power, raise both numerator and
denominator to power
Product‐to‐Power Rule
0 and
0 and
·
Ex:
If
If
0, and
Ex:
is a real number, then
When a product is raised to a power, raise each
factor to the power
Ex:
Negative Exponent
If
0, and
is a positive real number, then
and
Base to negative power moves from numerator to
denominator, or vice versa, the sign of power
changes.
Zero Exponent
If
0, then
1
Any nonzero number to the zero power equals 1.
Ex: 5
Ex: 5
5·
1
5·1
Ex: 3
Ex:
5