What is the value of $5^{-2}$?

A negative exponent gives the **reciprocal** of the positive-exponent power: $5^{-2} = \dfrac{1}{5^{2}} = \dfrac{1}{25}$. The negative sign in the **exponent** is *not* a negative sign on the value — it only inverts. - Trap A ($-25$) treats the exponent as a multiplier on the sign. - Trap B ($-10 = -5 \cdot 2$) treats exponent as multiplication. - Trap C ($1/10$) is $\dfrac{1}{2 \cdot 5}$ — confuses base with exponent product. Rule: for $a \ne 0$ and integer $n$, $a^{-n} = \dfrac{1}{a^{n}}$.