Question

rewrite the expression with rational exponents.
\\(\sqrt6{x^7}\\)
\\(\sqrt6{x^7}=\square\\)

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical expression \(\sqrt[n]{a^m}\) to a rational exponent is \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\).

Step2: Apply the rule to the given expression

For the expression \(\sqrt[6]{x^7}\), here \(n = 6\) (the index of the radical) and \(m = 7\) (the exponent of the base inside the radical). Using the rule \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), we substitute \(a=x\), \(m = 7\) and \(n=6\). So we get \(x^{\frac{7}{6}}\).

Answer:

\(x^{\frac{7}{6}}\)