Question

radicals introduction to simplifying a radical expression with an even exponent simplify. \\(\sqrt{y^{14}}\\) assume that the variable represents a positive real number.

Explanation:

Step1: Recall the property of square roots

For a non - negative real number \(a\) and an even positive integer \(n\), \(\sqrt{a^{n}}=a^{\frac{n}{2}}\) when \(a\geq0\). In the expression \(\sqrt{y^{14}}\), we can apply this property.

Step2: Apply the property to the given expression

Here, \(a = y\) and \(n = 14\). So we calculate \(\frac{14}{2}=7\). Then \(\sqrt{y^{14}}=y^{7}\) since \(y\) is a positive real number (so we don't have to consider the absolute value as \(y\) is non - negative in this context).

Answer:

\(y^{7}\)