Question
Simplify. \[ \left(4 a^{2}\right)^{2} a^{9}+a^{5} a^{8} \]
Ask by French Zimmerman. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \(17a^{13}\).
Solution
Calculate or simplify the expression \( (4a^2)^2 * a^9 + a^5 * a^8 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(4a^{2}\right)^{2}a^{9}+a^{5}\times a^{8}\)
- step1: Multiply the terms:
\(16a^{13}+a^{5}\times a^{8}\)
- step2: Multiply the terms:
\(16a^{13}+a^{13}\)
- step3: Collect like terms:
\(\left(16+1\right)a^{13}\)
- step4: Add the numbers:
\(17a^{13}\)
The simplified expression is \(17a^{13}\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \(\left(4 a^{2}\right)^{2} a^{9}+a^{5} a^{8}\), we can start by simplifying each term separately. First, let's simplify \(\left(4 a^{2}\right)^{2}\): \[ \left(4 a^{2}\right)^{2} = 4^{2} (a^{2})^{2} = 16 a^{4} \] Now, we can multiply this by \(a^{9}\): \[ 16 a^{4} a^{9} = 16 a^{4+9} = 16 a^{13} \] Next, we simplify the second term \(a^{5} a^{8}\): \[ a^{5} a^{8} = a^{5+8} = a^{13} \] Now, we can combine both simplified terms: \[ 16 a^{13} + a^{13} = (16 + 1) a^{13} = 17 a^{13} \] Thus, the simplified expression is: \[ \boxed{17 a^{13}} \]
