Question

rewrite the expression (sqrt7{x^{2}}) using a fractional exponent.
(sqrt7{x^{2}} = x^{square})
(simplify your answer.)

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to a fractional exponent is \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), where \(n\) is the index of the radical and \(m\) is the exponent of the base inside the radical.

Step2: Apply the rule to the given expression

For the expression \(\sqrt[7]{x^2}\), here \(n = 7\) (the index of the 7th root) and \(m=2\) (the exponent of \(x\) inside the radical). Using the rule \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), we substitute \(a = x\), \(m = 2\) and \(n=7\). So \(\sqrt[7]{x^2}=x^{\frac{2}{7}}\).

Answer:

\(\frac{2}{7}\)