Be careful 5^(a−2) = 1/125. Find 2a

We know that $125 = 5^3$. Using the property $x^{-n} = \frac{1}{x^n}$, we can write $\frac{1}{125}$ as $5^{-3}$.

$$5^{a-2} = \frac{1}{5^3}$$ $$5^{a-2} = 5^{-3}$$

Since the bases are the same, the exponents must be equal.

$$a-2 = -3$$

Add 2 to both sides of the equation.

$$a = -3 + 2$$ $$a = -1$$

Substitute the value of $a$ into $2a$.

$$2a = 2(-1)$$ $$2a = -2$$

The final answer is $-2$.