To determine the result of the arithmetic operation [tex]\( 3^{\text{} \, 4} \)[/tex]:
1. We begin with the base number [tex]\( 3 \)[/tex].
2. The exponent [tex]\( 4 \)[/tex] indicates that we need to multiply the base number [tex]\( 3 \)[/tex] by itself a total of 4 times.
3. This can be written as [tex]\( 3 \times 3 \times 3 \times 3 \)[/tex].
Let's multiply step-by-step:
- First, multiply [tex]\( 3 \)[/tex] by [tex]\( 3 \)[/tex]:
[tex]\[ 3 \times 3 = 9 \][/tex]
- Next, multiply the result by another [tex]\( 3 \)[/tex]:
[tex]\[ 9 \times 3 = 27 \][/tex]
- Finally, multiply the result by [tex]\( 3 \)[/tex] one more time:
[tex]\[ 27 \times 3 = 81 \][/tex]
Thus, the result of the arithmetic operation [tex]\( 3^{\text{} \, 4} \)[/tex] is [tex]\( \boxed{81} \)[/tex].
