Chan Adkins
04/29/2024 · Senior High School
\( (-9+3.2)^{5}.((-3)^{2})^{4} \)
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Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( (-9 + 3.2)^{5} \cdot ((-3)^{2})^{4} \), we will break it down step by step.
1. **Calculate \( -9 + 3.2 \)**:
\[
-9 + 3.2 = -5.8
\]
2. **Calculate \( (-5.8)^{5} \)**:
\[
(-5.8)^{5} = -5.8 \times -5.8 \times -5.8 \times -5.8 \times -5.8
\]
This is a negative number raised to an odd power, so the result will be negative.
3. **Calculate \( (-3)^{2} \)**:
\[
(-3)^{2} = 9
\]
4. **Calculate \( (9)^{4} \)**:
\[
9^{4} = 9 \times 9 \times 9 \times 9 = 6561
\]
5. **Combine the results**:
Now we have:
\[
(-5.8)^{5} \cdot 6561
\]
6. **Calculate \( (-5.8)^{5} \)**:
\[
(-5.8)^{5} = -5.8 \times -5.8 \times -5.8 \times -5.8 \times -5.8
\]
Calculating \( (-5.8)^{2} \):
\[
(-5.8)^{2} = 33.64
\]
Then,
\[
(-5.8)^{4} = (33.64)^{2} = 1135.8096
\]
Finally,
\[
(-5.8)^{5} = -5.8 \times 1135.8096 \approx -6596.696
\]
7. **Final multiplication**:
Now we multiply:
\[
-6596.696 \cdot 6561 \approx -43200000
\]
Thus, the final result of the expression \( (-9 + 3.2)^{5} \cdot ((-3)^{2})^{4} \) is approximately:
\[
\boxed{-43200000}
\]
Quick Answer
The result of the expression \( (-9 + 3.2)^{5} \cdot ((-3)^{2})^{4} \) is approximately \(-43200000\).
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