What is the value of $$ a^0 $$ when $$ a
eq 0 $$?

Question

What is the value of $$ a^0 $$ when $$ a 
eq 0 $$?

UpStudy AI · Accepted Answer

The value of $$ a^0 $$ for any non-zero number $$ a $$ is defined to be 1. This is based on the properties of exponents.

To understand why, consider the following:

1. The exponent rule states that $$ a^m \cdot a^n = a^{m+n} $$.
2. If we let $$ m = 1 $$ and $$ n = -1 $$, we have:
   $$
   a^1 \cdot a^{-1} = a^{1 + (-1)} = a^0
   $$
3. Since $$ a^{-1} = \frac{1}{a} $$, we can rewrite the left side:
   $$
   a \cdot \frac{1}{a} = 1
   $$
4. Therefore, we conclude that:
   $$
   a^0 = 1
   $$

Thus, the value of $$ a^0 $$ when $$ a \neq 0 $$ is $$ \boxed{1} $$.
$$ a^0 = 1 $$ when $$ a \neq 0 $$.

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