The value of $3^4$ is $81$.

To grasp why $3^4$ equals $81$, let’s break down the expression. The notation $3^4$ signifies that the number $3$ is multiplied by itself four times. This represents an exponentiation, where $3$ is the base and $4$ is the exponent. We can express this calculation as follows:

First, we multiply the first two $3$s:

Next, we take that result and multiply it by the next $3$:

Finally, we multiply that result by the last $3$:

Thus, we can confirm that $3^4$ equals $81$. Exponentiation is a method used to express repeated multiplication of the same number. It is a fundamental concept in mathematics, particularly valuable in algebra and advanced mathematics. Mastering how to work with exponents will enhance your ability to tackle more complex problems involving powers and roots.