Solve the equation. Simplify the answer as much as possible. $$ 5^{-3 a-2}=625 $$ The solution set is $$ \{\square\} $$

Question

UpStudy AI · Accepted Answer

We start with the equation

$$
5^{-3a-2} = 625.
$$

Recognize that $$625$$ can be written as a power of $$5$$:

$$
625 = 5^4.
$$

Thus, the equation becomes

$$
5^{-3a-2} = 5^4.
$$

Since the bases are the same and nonzero, the exponents must be equal:

$$
-3a - 2 = 4.
$$

Now, solve this linear equation for $$a$$:

$$
-3a = 4 + 2,
$$

$$
-3a = 6,
$$

$$
a = \frac{6}{-3},
$$

$$
a = -2.
$$

The solution set is $$\{-2\}$$.
The solution is $$ a = -2 $$.

Solve the equation. Simplify the answer as much as possible.

The solution set is