Question
Add. Assume that all variables represent positive real numbers. \( \frac{\sqrt[3]{8 x^{4}}}{13}+\frac{4 x \sqrt[3]{x}}{13} \) \( \frac{\sqrt[3]{8 x^{4}}}{13}+\frac{4 x \sqrt[3]{x}}{13}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)
Ask by Mckenzie Coles. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{6x\sqrt[3]{x}}{13} \).
Solution
Calculate or simplify the expression \( \frac{\sqrt[3]{8x^4}}{13}+\frac{4x\sqrt[3]{x}}{13} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\sqrt[3]{8x^{4}}}{13}+\frac{4x\sqrt[3]{x}}{13}\)
- step1: Simplify the root:
\(\frac{2x\sqrt[3]{x}}{13}+\frac{4x\sqrt[3]{x}}{13}\)
- step2: Transform the expression:
\(\frac{2x\sqrt[3]{x}+4x\sqrt[3]{x}}{13}\)
- step3: Add the terms:
\(\frac{6\sqrt[3]{x}\times x}{13}\)
The simplified expression is \( \frac{6\sqrt[3]{x} \times x}{13} \).
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Simplify this solution Beyond the Answer
To simplify the expression \(\frac{\sqrt[3]{8 x^{4}}}{13}+\frac{4 x \sqrt[3]{x}}{13}\), we start with each term. The first term is: \[ \frac{\sqrt[3]{8 x^{4}}}{13} = \frac{\sqrt[3]{8} \sqrt[3]{x^{4}}}{13} = \frac{2 \cdot x^{4/3}}{13} = \frac{2 x^{4/3}}{13} \] The second term is: \[ \frac{4 x \sqrt[3]{x}}{13} = \frac{4 x^{1} x^{1/3}}{13} = \frac{4 x^{(1 + 1/3)}}{13} = \frac{4 x^{4/3}}{13} \] Now we add the two terms together: \[ \frac{2 x^{4/3}}{13} + \frac{4 x^{4/3}}{13} = \frac{(2 + 4) x^{4/3}}{13} = \frac{6 x^{4/3}}{13} \] Therefore, the simplified expression is: \[ \frac{6 x^{4/3}}{13} = \square \] So, the final answer is: \[ \frac{6 x^{4/3}}{13} \]
