Convert x^(1/7) to radical form.
Understand the Problem
The question asks to convert an expression from exponential form to radical form. The expression is x raised to the power of 1/7.
Answer
$\sqrt[7]{x}$
Answer for screen readers
$\sqrt[7]{x}$
Steps to Solve
- Understanding Exponential Form
$x^{\frac{1}{7}}$ is in exponential form, where $x$ is the base and $\frac{1}{7}$ is the exponent.
- Relating Exponential and Radical Forms
The general rule to convert from exponential to radical form is: $x^{\frac{m}{n}} = \sqrt[n]{x^m}$
- Applying the Rule
In our case, $m = 1$ and $n = 7$. Applying the rule, we get: $x^{\frac{1}{7}} = \sqrt[7]{x^1}$
- Simplifying the Radical Form
Since $x^1 = x$, we can simplify the radical form to: $\sqrt[7]{x}$
$\sqrt[7]{x}$
More Information
The number '7' in $\sqrt[7]{x}$ is called the index of the radical. It indicates the root we are taking (in this case, the 7th root).
Tips
A common mistake is to misinterpret the position of the numerator and denominator in the fractional exponent when converting to radical form. The denominator becomes the index of the radical, and the numerator becomes the exponent of the radicand (the expression inside the radical). For instance, mistaking $x^{\frac{1}{7}}$ for $\sqrt[1]{x^7}$ would be incorrect.
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