Question
Simplify the expression completely: \( \frac{1}{2 y^{-4}}=\square \)
Ask by Simpson Nunez. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is \( \frac{y^{4}}{2} \).
Solution
To simplify the expression:
\[
\frac{1}{2 y^{-4}}
\]
Follow these steps:
1. **Understand Negative Exponents:**
\[
y^{-4} = \frac{1}{y^4}
\]
2. **Substitute Back into the Expression:**
\[
\frac{1}{2 y^{-4}} = \frac{1}{2 \cdot \frac{1}{y^4}} = \frac{1}{\frac{2}{y^4}}
\]
3. **Simplify the Fraction:**
\[
\frac{1}{\frac{2}{y^4}} = \frac{y^4}{2}
\]
So, the simplified form of the expression is:
\[
\boxed{\dfrac{y^{4}}{2}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify the expression \( \frac{1}{2 y^{-4}} \), we can first recall that \( y^{-4} \) is equivalent to \( \frac{1}{y^4} \). Thus, the expression can be rewritten as follows: \[ \frac{1}{2 y^{-4}} = \frac{1}{2 \cdot \frac{1}{y^4}} = \frac{y^4}{2} \] So, the simplified expression is: \[ \frac{y^4}{2} \]
