# Write each radical expression using exponents and each exponential expression using radicals. Radical expression Exponential expression sqrt[3]{y^{4}}

Question
Write each radical expression using exponents and each exponential expression using radicals. Radical expression Exponential expression $$\sqrt[3]{y^{4}}$$

2021-01-23
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 $$\sqrt[3]{y^{4}}\ \text{as}\ y^{\frac{4}{3}}$$

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