Phillips Bates
07/30/2024 · Senior High School
6) \( 3,24 m^{6} n^{12}=(\ldots)^{2} \)
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Tutor-Verified Answer
Step-by-step Solution
To express \( 3.24 m^{6} n^{12} \) as a square, we need to find a form \( (a \cdot b)^{2} \) such that when expanded, it equals \( 3.24 m^{6} n^{12} \).
1. **Factor the coefficient**:
We start with the coefficient \( 3.24 \). We can express it as a square:
\[
3.24 = (1.8)^{2}
\]
2. **Factor the variables**:
Next, we look at the variables \( m^{6} \) and \( n^{12} \):
- \( m^{6} = (m^{3})^{2} \)
- \( n^{12} = (n^{6})^{2} \)
3. **Combine everything**:
Now we can combine these results:
\[
3.24 m^{6} n^{12} = (1.8)^{2} (m^{3})^{2} (n^{6})^{2}
\]
4. **Write it as a single square**:
We can factor this into a single square:
\[
3.24 m^{6} n^{12} = (1.8 m^{3} n^{6})^{2}
\]
Thus, the expression \( 3.24 m^{6} n^{12} \) can be written as:
\[
(1.8 m^{3} n^{6})^{2}
\]
Quick Answer
\( 3.24 m^{6} n^{12} = (1.8 m^{3} n^{6})^{2} \)
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