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Step 1:I'll solve this step by step, using proper LaTeX notation:
Step 2:: Understand the Radical Form
The radical form of a fractional exponent involves converting the exponent to a radical (root) expression.
Step 3:: Recall the Conversion Rule
For a fractional exponent $$x^{a/b}$$, the radical form is $$\sqrt[b]{x^{a}}
Step 4:: Apply the Rule to x^{4 / 5}
- So we'll convert $$x^{4/5}$$ to $$\sqrt[5]{x^{4}}
- The numerator is 4 - The denominator is 5
Step 5:: Simplify the Radical
The radical form of $$x^{4/5}$$ is $$\sqrt[5]{x^{4}}
Final Answer
Key Insights: - The denominator (5) becomes the root index - The numerator (4) becomes the power inside the radical - This preserves the original fractional exponent's value
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