Question
Apply the Quotient of Powers Property to simplify: \( \frac{y^{8}}{y^{3}} \)
Ask by Rodriquez Tyler. in Italy
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( y^{5} \)
Solution
To simplify the expression \( \frac{y^{8}}{y^{3}} \) using the **Quotient of Powers Property**, follow these steps:
### **Quotient of Powers Property**
The Quotient of Powers Property states that when you divide two expressions with the same base, you can subtract the exponents:
\[
\frac{a^{m}}{a^{n}} = a^{m-n}
\]
### **Applying the Property**
Given the expression:
\[
\frac{y^{8}}{y^{3}}
\]
1. **Identify the base and the exponents:**
- **Base:** \( y \)
- **Exponent in the numerator (top):** 8
- **Exponent in the denominator (bottom):** 3
2. **Subtract the exponents:**
\[
y^{8-3} = y^{5}
\]
### **Simplified Expression**
\[
\frac{y^{8}}{y^{3}} = y^{5}
\]
So, the simplified form of \( \frac{y^{8}}{y^{3}} \) is **\( y^{5} \)**.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify \( \frac{y^{8}}{y^{3}} \), you can use the Quotient of Powers Property, which states that when you divide powers with the same base, you subtract the exponents. So, you would subtract 3 from 8, giving you \( y^{8-3} = y^{5} \). The simplified form of \( \frac{y^{8}}{y^{3}} \) is \( y^{5} \). Simplifying this expression is great practice for understanding how to handle exponents efficiently!
