Question
Simplify. \( \frac{b^{6} a^{3}}{b^{2} a^{5}} \)
Ask by Graham Davison. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(\frac{b^{4}}{a^{2}}\)
Solution
To simplify the expression \( \frac{b^{6} a^{3}}{b^{2} a^{5}} \), you can apply the laws of exponents. Here's a step-by-step breakdown:
1. **Divide the bases with exponents:**
- For the \( b \) terms: \( \frac{b^{6}}{b^{2}} = b^{6-2} = b^{4} \)
- For the \( a \) terms: \( \frac{a^{3}}{a^{5}} = a^{3-5} = a^{-2} \)
2. **Combine the results:**
- \( b^{4} \cdot a^{-2} \)
3. **Express with positive exponents:**
- \( b^{4} \cdot \frac{1}{a^{2}} = \frac{b^{4}}{a^{2}} \)
So, the simplified form of the expression is:
\[
\frac{b^{4}}{a^{2}}
\]
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Simplify this solution Extra Insights
To simplify the expression \( \frac{b^{6} a^{3}}{b^{2} a^{5}} \), you can subtract the exponents of like bases. For \( b \), you have \( 6 - 2 = 4 \), and for \( a \), you have \( 3 - 5 = -2 \). This means the expression simplifies to: \( b^{4} a^{-2} \) You can further express \( a^{-2} \) as \( \frac{1}{a^{2}} \), so the final simplified form is: \( \frac{b^{4}}{a^{2}} \).
