Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\left(\frac{4}{7 y}\right)^{2} = \frac{16}{49 y^{2}}
\]
Solution
To simplify the expression \( \left(\frac{4}{7 y}\right)^{2} \), follow these steps:
1. **Apply the Exponent to Both the Numerator and the Denominator:**
\[
\left(\frac{4}{7 y}\right)^{2} = \frac{4^{2}}{(7 y)^{2}}
\]
2. **Calculate the Squares:**
- \(4^{2} = 16\)
- \((7 y)^{2} = 49 y^{2}\)
3. **Combine the Results:**
\[
\frac{4^{2}}{(7 y)^{2}} = \frac{16}{49 y^{2}}
\]
**Final Simplified Form:**
\[
\left(\frac{4}{7 y}\right)^{2} = \frac{16}{49 y^{2}}
\]
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Simplify this solution The Deep Dive
Let's simplify \( \left(\frac{4}{7 y}\right)^{2} \). To do this, we square both the numerator and the denominator separately. So, \[ \left(\frac{4}{7 y}\right)^{2} = \frac{4^2}{(7 y)^2} = \frac{16}{49 y^2} \] And there you have it! The expression simplifies beautifully to \( \frac{16}{49 y^2} \). Now you're all set to tackle any more quadratic fractions that come your way! Remember, squaring a fraction involves squaring each part separately. How cool is that?
