Question

How do you express `sqrtt` as a fractional exponent?

Answer 1

`t^(1/2)`

Explanation:

`sqrt t`

is actually

`2_sqrt t`

Now i just throw the outside 2 to the other side as the denominator. of `t^1`

`t^(1/2)`

Answer 2

`t^(1/2)`

Explanation:

When taking the square root of something you raise its power to `1/2`. If you have a digital calculator you can try it out yourself.

This is because of the Laws of exponents:

`a^n times a^m=a^(n+m)`

We know that:

`sqrtt times sqrtt=t`

And from the Laws of exponents, we know that the sum of the two exponents should equal 1. In the case of
`sqrtt times sqrtt` this is equal to `t`, which is essentially `t^1`.

Using exponents we can rewrite the multiplications of the roots presented above:

`t^xtimest^x=t^1`

And because the sum of our exponents on the left should equal 1, we can solve for the unknown.

`x+x=1`
`x=(1/2)`

Therefore we can conclude that:
`t^(1/2)=sqrtt`