Explore how radicals can be expressed as rational exponents. Compare equivalent forms to see how fractional powers relate to roots.
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
In your own words, why does it make sense to define [math]a^{\frac{1}{4}}=\sqrt[4]{a}[/math]?
Is it correct to write [math]\sqrt{a}=a^{\frac{1}{2}}[/math] when a is a negative number? What about [math]\sqrt[3]{a}=a^{\frac{1}{3}}[/math]? Explain your reasoning.