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}}

Answer 1

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 $a \geq 0$ .

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 $\sqrt[3]{y^{4}} as y^{\frac{4}{3}}$

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

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