Question
(3) \( \frac{6 a^{4}+9 a^{4}}{5 a^{2}} \)
Ask by Vega Dawson. in South Africa
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( 3a^{2} \).
Solution
To simplify the expression:
\[
\frac{6 a^{4} + 9 a^{4}}{5 a^{2}}
\]
**Step 1: Combine Like Terms in the Numerator**
Both terms in the numerator have the same variable raised to the same power (\(a^4\)). You can add their coefficients directly.
\[
6 a^{4} + 9 a^{4} = (6 + 9) a^{4} = 15 a^{4}
\]
**Step 2: Rewrite the Expression with the Combined Numerator**
\[
\frac{15 a^{4}}{5 a^{2}}
\]
**Step 3: Simplify the Fraction**
- **Divide the coefficients:** \( \frac{15}{5} = 3 \)
- **Subtract the exponents when dividing like bases:** \( a^{4} \div a^{2} = a^{4-2} = a^{2} \)
\[
\frac{15 a^{4}}{5 a^{2}} = 3 a^{2}
\]
**Final Simplified Expression:**
\[
3 a^{2}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify the expression \( \frac{6 a^{4}+9 a^{4}}{5 a^{2}} \), first, combine the terms in the numerator: \( 6 a^{4} + 9 a^{4} = 15 a^{4} \). Now the expression looks like \( \frac{15 a^{4}}{5 a^{2}} \). Next, simplify the fraction: \( \frac{15}{5} = 3 \) and \( \frac{a^{4}}{a^{2}} = a^{4-2} = a^{2} \). So the simplified expression is \( 3 a^{2} \). Final answer: \( 3 a^{2} \)
