Question
QUESTION 29 Simplify \[ \left(4 x^{2}\right)^{3} \] A \( 4 x^{6} \) B \( 64 x^{6} \) c \( 4 x^{5} \) D \( 12 x^{6} \)
Ask by Campbell Hill. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form is \(64x^{6}\).
Solution
To simplify \(\left(4 x^{2}\right)^{3}\), follow these steps:
1. **Apply the exponent to both the coefficient and the variable:**
\[
\left(4 x^{2}\right)^{3} = 4^{3} \times \left(x^{2}\right)^{3}
\]
2. **Calculate each part separately:**
- \(4^{3} = 64\)
- \(\left(x^{2}\right)^{3} = x^{2 \times 3} = x^{6}\)
3. **Combine the results:**
\[
64 \times x^{6} = 64x^{6}
\]
**Answer:**
**B \( 64 x^{6} \)**
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Simplify this solution Extra Insights
To simplify \((4 x^{2})^{3}\), you can use the power of a product rule, which states that \((ab)^{n} = a^{n} b^{n}\). Here, \(a = 4\) and \(b = x^{2}\). First, calculate \(4^{3}\): \[ 4^{3} = 64 \] Next, apply the exponent to \(x^{2}\): \[ (x^{2})^{3} = x^{2 \cdot 3} = x^{6} \] Now, combine these results: \[ (4 x^{2})^{3} = 64 x^{6} \] So the correct answer is \(B\) \(64 x^{6}\).
