25) $$ 10^{-2 b-3}=10^{-3 b} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
10^{-2b - 3} = 10^{-3b}
$$

**Step 1: Recognize the Property of Exponents**

Since the bases are the same (both are 10) and greater than 0, we can set the exponents equal to each other:

$$
-2b - 3 = -3b
$$

**Step 2: Solve for $$ b $$**

1. **Add $$ 3b $$ to both sides** to get all $$ b $$ terms on one side:

$$
-2b - 3 + 3b = -3b + 3b
$$

$$
b - 3 = 0
$$

2. **Add 3 to both sides** to isolate $$ b $$:

$$
b = 3
$$

**Solution:**

$$
b = 3
$$
$$ b = 3 $$

25) \( 10^{-2 b-3}=10^{-3 b} \)