Question

rewrite the expression as an equivalent radical expression.
w^{\frac{1}{3}}
show your work here
hint: to add the nth root symbol (\sqrtn{\square}), type
oot\

Explanation:

Step1: Recall the exponent - radical relationship

The formula that relates exponents and radicals is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (when \(n>0\) and \(a\) is a real number for which the expression is defined). In the given expression \(w^{\frac{1}{3}}\), we have \(a = w\), \(m = 1\) and \(n=3\).

Step2: Apply the formula

Using the formula \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), substitute \(a = w\), \(m = 1\) and \(n = 3\). We get \(\sqrt[3]{w^{1}}\) which simplifies to \(\sqrt[3]{w}\).

Answer:

\(\sqrt[3]{w}\)