Question

Find the cube root of 81: 3^√81 .

Answer 1

To find the cube root of 81, we start by rewriting it as \( 3^{\sqrt{81}} \).

First, we calculate \( \sqrt{81} \):

\[
\sqrt{81} = 9
\]

Now substitute this back into the expression:

\[
3^{\sqrt{81}} = 3^9
\]

Next, we want to find the cube root of \( 81 \). The cube root of a number \( x \) can be expressed as \( x^{1/3} \).

Thus, we need to find:

\[
81^{1/3}
\]

We can rewrite 81 as a power of 3:

\[
81 = 3^4
\]

Then the cube root becomes:

\[
81^{1/3} = (3^4)^{1/3} = 3^{4/3}
\]

Hence, \( 3^{\sqrt{81}} \) simplifies to \( 3^9 \), and the cube root of 81 is \( 3^{4/3} \).

So, the cube root of 81 is:

\[
\boxed{3^{4/3}}
\]