Question
Simplify fully: \( \frac{4 a^{5}}{8 a^{3} \times 2 a} \)
Ask by Mitchell Bowers. in Australia
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{a}{4} \).
Solution
1. Write the given expression:
\[
\frac{4a^{5}}{8a^{3} \times 2a}
\]
2. Simplify the denominator by multiplying:
\[
8a^{3} \times 2a = 16a^{3+1} = 16a^4
\]
3. Substitute the simplified denominator back into the expression:
\[
\frac{4a^{5}}{16a^{4}}
\]
4. Simplify the coefficients:
\[
\frac{4}{16} = \frac{1}{4}
\]
5. Simplify the powers of \(a\) using the division rule \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{a^{5}}{a^{4}} = a^{5-4} = a
\]
6. Combine the simplified coefficient and variable:
\[
\frac{a}{4}
\]
The fully simplified expression is:
\[
\frac{a}{4}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify the expression \( \frac{4 a^{5}}{8 a^{3} \times 2 a} \), we start by simplifying the denominator: First, multiply \( 8 a^{3} \times 2 a \): \[ 8 \times 2 = 16 \quad \text{and} \quad a^{3} \times a = a^{4} \quad \Rightarrow \quad 8 a^{3} \times 2 a = 16 a^{4} \] Now we rewrite the original expression: \[ \frac{4 a^{5}}{16 a^{4}} \] Next, we can simplify the coefficients and the powers of \( a \): \[ \frac{4}{16} = \frac{1}{4} \quad \text{and} \quad \frac{a^{5}}{a^{4}} = a^{5-4} = a^{1} = a \] Combining these results gives: \[ \frac{1}{4} a = \frac{a}{4} \] Thus, the fully simplified expression is: \[ \frac{a}{4} \]
