Question

nal exponents
nverting between radical and exponential form
what is $15^{\frac{1}{3}}$ in radical form?
$\sqrt\frac{1}{3}{15}$ $\sqrt3{15}$ $\sqrt10{3}$

Explanation:

Step1: Recall the formula for converting exponents to radicals

The formula for converting \( a^{\frac{m}{n}} \) to radical form is \( \sqrt[n]{a^m} \). When \( m = 1 \), it simplifies to \( \sqrt[n]{a} \). Here, we have \( 15^{\frac{1}{3}} \), so \( a = 15 \), \( m = 1 \), and \( n = 3 \).

Step2: Apply the formula

Using the formula \( a^{\frac{1}{n}}=\sqrt[n]{a} \), substituting \( a = 15 \) and \( n = 3 \), we get \( \sqrt[3]{15} \).

Answer:

\( \sqrt[3]{15} \) (the middle option: \( \sqrt[3]{15} \))