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

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

For any rational exponent ${}^{m}{/}_{n}$ in lowest terms, where m and n are integers and $n>0$, we define or equivalently ${a}^{{}^{m}{/}_{n}}=\sqrt[n]{{a}^{m}}$.

If n is even, then we require that $a\ge 0$.

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, $\sqrt[3]{{y}^{4}}=\left({y}^{4}{\right)}^{\frac{1}{3}}$
$={y}^{\frac{4}{3}}$ Therefore, using exponential notation, we can write