Question
(5xA \( \frac{x^{\frac{11}{4}}}{x^{\frac{3}{4}}} \) Simplify. Assume all variables are positive.
Ask by Mullins Hobbs. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \(5x^3\).
Solution
To simplify the expression:
\[ 5x \cdot \left( \frac{x^{\frac{11}{4}}}{x^{\frac{3}{4}}} \right) \]
**Step 1: Simplify the Fraction**
Use the property of exponents \(\frac{x^a}{x^b} = x^{a-b}\):
\[
\frac{x^{\frac{11}{4}}}{x^{\frac{3}{4}}} = x^{\frac{11}{4} - \frac{3}{4}} = x^{\frac{8}{4}} = x^2
\]
**Step 2: Multiply by \(5x\)**
\[
5x \cdot x^2 = 5x^{1+2} = 5x^3
\]
**Final Simplified Expression:**
\[
5x^3
\]
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Simplify this solution Beyond the Answer
To simplify \( \frac{x^{\frac{11}{4}}}{x^{\frac{3}{4}}} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). Subtract the exponents: \( \frac{11}{4} - \frac{3}{4} = \frac{8}{4} = 2 \). Therefore, \( \frac{x^{\frac{11}{4}}}{x^{\frac{3}{4}}} = x^{2} \). Now, multiplying by \( 5xA \), you get the simplified expression: \( 5Ax^2 \). So, the final answer is \( 5Ax^2 \).
