Question

Simplify the expression below using order of operations.
start fraction, 3, plus, left parenthesis, minus, 3, right parenthesis, divided by, minus, 3, plus, 1, end fraction, plus, start fraction, 9, to the power 1 , minus, 3, squared, divided by, minus, 7, minus, 8, end fraction
−3+1
3+(−3)
​
+
−7−8
9
1
−3
2

​

Answer 1

To simplify the given expression, we start by rewriting it for clarity. The expression is:

\[
\frac{3 + (-3)}{-3 + 1} + \frac{9^{1 - 3^2}}{-7 - 8}
\]

Let's simplify each part step by step:

### Step 1: Simplify the first fraction

1. **Numerator:**
\[
3 + (-3) = 0
\]

2. **Denominator:**
\[
-3 + 1 = -2
\]

Putting it together, the first fraction becomes:
\[
\frac{0}{-2} = 0
\]

### Step 2: Simplify the second fraction

1. **Exponent Simplification:**
\[
3^2 = 9
\]
Therefore:
\[
1 - 3^2 = 1 - 9 = -8
\]

2. **Calculating \(9^{-8}\):**
\[
9^{-8} = \frac{1}{9^8}
\]

3. **Denominator:**
\[
-7 - 8 = -15
\]

Now, substituting:
\[
\frac{9^{-8}}{-15} = \frac{1/9^8}{-15} = -\frac{1}{15 \cdot 9^8}
\]

### Step 3: Combine both parts
Now we put together the simplified parts:
\[
0 + \left(-\frac{1}{15 \cdot 9^8}\right) = -\frac{1}{15 \cdot 9^8}
\]

### Conclusion
Thus, the simplified expression is:
\[
-\frac{1}{15 \cdot 9^8}
\]