If \( a \neq 0 \), what is the value of \( a^{m} \cdot a^{-m} \) ? How do you know?

To find the value of \( a^{m} \cdot a^{-m} \), we can use the properties of exponents. Recall that when multiplying two expressions with the same base, we can add their exponents: \[ a^{m} \cdot a^{-m} = a^{m + (-m)} = a^{m - m} = a^{0} \] Now, we know from the properties of exponents that any non-zero number raised to the power of zero is equal to 1: \[ a^{0} = 1 \quad \text{(since \( a \neq 0 \))} \] Thus, we conclude that: \[ a^{m} \cdot a^{-m} = 1 \] So, the value of \( a^{m} \cdot a^{-m} \) is \( \boxed{1} \).