Question

simplify.
\sqrt{81z^{14}}
assume that the variable z represe

Explanation:

Step1: Simplify the square root of 81

The square root of 81 is 9, since \(9\times9 = 81\). So we have \(\sqrt{81z^{14}}=\sqrt{81}\times\sqrt{z^{14}}\).

Step2: Simplify the square root of \(z^{14}\)

Using the property of exponents \(\sqrt{a^m}=a^{\frac{m}{2}}\) (for \(a\geq0\) and \(m\) even), for \(z^{14}\), we get \(\sqrt{z^{14}} = z^{\frac{14}{2}}=z^{7}\).

Step3: Combine the results

Multiply the results from Step1 and Step2: \(9\times z^{7}=9z^{7}\).

Answer:

\(9z^{7}\)