Question

Simplify the expression below using order of operations.
start fraction, 2, squared, divided by, 9, minus, 2, cubed, end fraction, plus, left parenthesis, minus, 3, right parenthesis
9−2
3

2
2

​
+(−3)

Answer 1

To simplify the expression \(\frac{2^2}{9 - 2^3} + (-3)\), we will follow the order of operations.

1. **Calculate the powers:**
- \(2^2 = 4\)
- \(2^3 = 8\)

2. **Substitute back into the expression:**
\[
\frac{4}{9 - 8} + (-3)
\]

3. **Calculate the denominator:**
\[
9 - 8 = 1
\]

4. **Substitute back into the expression:**
\[
\frac{4}{1} + (-3)
\]

5. **Calculate \(\frac{4}{1}\):**
\[
4 + (-3) = 4 - 3
\]

6. **Final calculation:**
\[
4 - 3 = 1
\]

Therefore, the simplified expression is \(\boxed{1}\).