Question

simplify.
$(-216)^{\frac{1}{3}}$

Explanation:

Step1: Recall the definition of rational exponents

For any real number \(a\) and positive integer \(n\), \(a^{\frac{1}{n}}=\sqrt[n]{a}\). So, \((-216)^{\frac{1}{3}}=\sqrt[3]{-216}\).

Step2: Find the cube root of -216

We know that \((-6)\times(-6)\times(-6)=(-6)^3=-216\). So, \(\sqrt[3]{-216} = - 6\).

Answer:

\(-6\)