Question

question
express \\(\left(14^{\frac{1}{3}}\
ight)^2\\) in simplest radical form.

Explanation:

Step1: Apply exponent power rule

When raising a power to a power, we multiply the exponents. The formula is \((a^m)^n = a^{m\times n}\). Here, \(a = 14\), \(m=\frac{1}{3}\), and \(n = 2\). So we calculate \(\frac{1}{3}\times2=\frac{2}{3}\), and we get \(14^{\frac{2}{3}}\).

Step2: Convert rational exponent to radical

Recall that \(a^{\frac{p}{q}}=\sqrt[q]{a^p}\) (where \(q\gt0\)). For \(14^{\frac{2}{3}}\), \(q = 3\) and \(p = 2\), so this is equivalent to \(\sqrt[3]{14^2}\).

Step3: Calculate \(14^2\)

\(14^2=14\times14 = 196\). So the expression becomes \(\sqrt[3]{196}\).

Answer:

\(\sqrt[3]{196}\)