Choose the largest value:
We need to find the largest of the given roots of 64:
Calculate 664:
664=641/6
Since 64=26, we have:
(26)1/6=2
Calculate 464:
464=641/4
Using the exponent 64=26, we get:
(26)1/4=26/4=21.5=28=2×2≈2.828
Calculate 364:
364=641/3
This simplifies to:
(26)1/3=26/3=22=4
Calculate 64:
64=641/2
This gives us:
(26)1/2=26/2=23=8
Now, let's compare these calculated values:
- 664=2
- 464≈2.828
- 364=4
- 64=8
Among these values, the largest value is 64, which equals 8.
Therefore, the largest value is 64.