Simplify 3^√54

Answer 1

To simplify 3^√54, we first need to simplify √54.

To do this, we can break down 54 into its prime factors: 54 = 2 * 3 * 3 * 3.

Taking the square root of this gives us √54 = √(2 * 3 * 3 * 3).

Simplifying further, we can split the square root: √(2 * 3 * 3 * 3) = √2 * √(3 * 3 * 3) = √2 * 3√3.

Now, we can substitute this back into the original expression: 3^√54 = 3^√(2 * 3 * 3 * 3) = 3^(√2 * 3√3).

Since we cannot further simplify this expression, the simplified form is 3^(√2 * 3√3).