Questions: If the nth root of a is a real number, then the cube root of a is equivalent to which of the following? a^(1/n) n^(1/6) a^n n^a

Transcript text: If the $n^{\text {th }}$ root of $a$ is a real number, then $\sqrt[3]{a}$ is equivalent to which of the following? $a^{\frac{1}{n}}$ $n^{\frac{1}{6}}$ $a^{n}$ $n^{a}$

Solution

Solution Steps

Step 1: Identify the Expression for the $ n^{\text{th}} $ Root

The $ n^{\text{th}} $ root of a number $ a $ is expressed as $ a^{\frac{1}{n}} $.

Step 2: Determine the Expression for the Cube Root

The cube root of $ a $, denoted as $ \sqrt[3]{a} $, is equivalent to $ a^{\frac{1}{3}} $.

Step 3: Compare the Given Options

$ a^{\frac{1}{n}} $ represents the $ n^{\text{th}} $ root of $ a $.
$ n^{\frac{1}{6}} $ is unrelated to the cube root of $ a $.
$ a^{n} $ is the $ n^{\text{th}} $ power of $ a $.
$ n^{a} $ is $ n $ raised to the power of $ a $.

The correct expression for the cube root of $ a $ is not explicitly listed among the options.

Final Answer

The correct answer is not listed among the options.

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