For any rational exponent \(m/_n\) in lowest terms, where m and n are
integers and \(n > 0\), we define
\(a\ m/_n=(\sqrt[n]{a})^{m}\) or equivalently \(a^{m/_n}=\sqrt[n]{{a}^{m}}\).
If n is even, then we require that \(a >= 0\).
Given:
\(\sqrt[3]{y^{4}}\)
Calculation:
Consider, \(\sqrt[3]{y^{4}}\)
From the above definition \(a^{m/_n}\) the exponential notation of
\(\sqrt[3]{y^{4}}\) is written as,
\(\sqrt[3]{y^{4}} = (y^{4})^{\frac{1}{3}}\)
\(= y^{\frac{4}{3}}\) Therefore, using exponential notation, we can write \(\sqrt[3]{y^{4}}\ \text{as}\ y^{\frac{4}{3}}\)
\(= y^{\frac{4}{3}}\) Therefore, using exponential notation, we can write \(\sqrt[3]{y^{4}}\ \text{as}\ y^{\frac{4}{3}}\)
