Question

rewrite $2^{\frac{4}{5}}$ in radical form.

Explanation:

Step1: Recall the exponent rule for radicals

The rule is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (or equivalently \((\sqrt[n]{a})^{m}\)), where \(a\) is the base, \(m\) is the numerator of the fraction exponent, and \(n\) is the denominator.

Step2: Apply the rule to \(2^{\frac{4}{5}}\)

Here, \(a = 2\), \(m = 4\), and \(n=5\). Using the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), we substitute the values: \(2^{\frac{4}{5}}=\sqrt[5]{2^{4}}\). We can also calculate \(2^{4}=16\), so it can be written as \(\sqrt[5]{16}\).

Answer:

\(\sqrt[5]{16}\) (or \(\sqrt[5]{2^{4}}\))