Question

simplify $1,296^{-\frac{1}{4}}$. write your answer in simplest radical form.

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\). So, \(1296^{-\frac{1}{4}}=\frac{1}{1296^{\frac{1}{4}}}\).

Step2: Simplify the fourth root

We need to find the fourth root of 1296. Let's recall that \(6^4 = 6\times6\times6\times6=1296\). So, \(1296^{\frac{1}{4}} = 6\).

Step3: Substitute back

Substituting \(1296^{\frac{1}{4}} = 6\) into \(\frac{1}{1296^{\frac{1}{4}}}\), we get \(\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)