For the arithmetic expression 4 · 4 · 4 · 4 = 256 a shorter notation was found in algebra, namely 44 = 256. Likewise, one writes for 3 · 3 · 3 · 3 = 81, 34 = 81, or instead 2 · 2 · 2 one writes 23.
23 is pronounced "two to the power of three".. Such an arithmetic structure is called a power. The number 2 is the base or fundamental number in this case, the number 3 is called exponent or exponent.
√8 means the "third root" from 8, That means, one looks for the number, multiplied by itself three times 8 results. That's obviously the number 2, because 2 · 2 · 2 = 8. Ebenso ergibt 4√256 (the fourth root 256) = 4, because 4 · 4 · 4 · 4 = 256.
Omits the "root exponent" left above the root sign, that's what the square root means, That means, the second root. So √9 = 3 and √4 = 2 or √81 = 9, because 3 · 3 = 9, 2 · 2 = 4 and 9 · 9 = 81 yields.·