Question
\begin{tabular}{|l} Directions: Simplify the \( f \) \\ \hline 1. \( \frac{y^{4}}{y^{2}} \) \\ \hline\end{tabular}
Ask by Flynn Tran. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \frac{y^{4}}{y^{2}} = y^{2} \)
Solution
To simplify the expression \( \frac{y^{4}}{y^{2}} \), you can use the **laws of exponents**. Specifically, when dividing powers with the same base, you subtract the exponents:
\[
\frac{y^{4}}{y^{2}} = y^{4 - 2} = y^{2}
\]
**Final Simplified Form:**
\[
y^{2}
\]
**Explanation:**
1. **Identify the base and exponents:**
- Base: \( y \)
- Exponents: \( 4 \) (numerator) and \( 2 \) (denominator)
2. **Apply the division rule for exponents:**
\[
\frac{y^{a}}{y^{b}} = y^{a - b}
\]
So,
\[
\frac{y^{4}}{y^{2}} = y^{4 - 2} = y^{2}
\]
3. **Result:**
The expression simplifies to \( y^{2} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
When simplifying \( \frac{y^{4}}{y^{2}} \), you can use the exponent rule which states that when dividing two powers with the same base, you subtract the exponents. So, \( y^{4-2} = y^{2} \). Therefore, the simplified form is \( y^{2} \), leaving you with a neat and tidy expression! And did you know that powers and exponents were developed independently by various cultures? Ancient Egyptians had their own methods, while the Hindu-Arabic numeral system laid the groundwork for our modern scientific notation! Mathematics has a rich history that makes it even more fascinating.
