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:

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