Question

how are exponents related to taking the root of a number?

Answer 1

Depending on how you look at it, they're the opposite.

Answer 2

taking the square root of a number is the inverse of squaring the number

Answer 3

the root of a number can be represent by raising a number to a fractional exponent

Answer 4

So, for example, if I raise a to the 8th power, \(a^8\), then I can get \(a\) back by taking the 8th root of the result: \(\sqrt[8]{a^8} = a\).

Answer 5

As Dockworker points out, another way to look at it is that a root is actually just another kind of exponent—a fractional one. So \(\sqrt[8]{a} = a^{\frac{1}{8}}\).

Answer 6

okay i understand now thank u very much

Answer 7

If we look at it this way, \(\sqrt[8]{a^8} = (a^8)^{\frac{1}{8}} = a^{\frac{8}{8}} = a^1 = a\).

Answer 8

Cool stuff. Make sure to give a medal by clicking “good answer” when you see a good answer :)

Answer 9

Aw thanks :)

Answer 10

haa anytime