Power with zero and negative integer exponent

The zero exponent

For any nonzero

a

we define:

a^0=1.

One intuition comes from

\dfrac{a^m}{a^m}=a^{m-m}=a^0

— when

a\neq0

the fraction on the left equals 1, so

a^0

is taken to match. The expression

0^0

is not assigned a numerical value in the school course (left undefined; contest math may use other conventions).

(-7)^0=1

, but in the separate expression

-7^0

exponentiation binds first, then the sign:

-1

For a variable, state the domain (

x\neq0

) explicitly if you divide by an expression with a power

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