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

2 Answers
Apr 5, 2018

#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)#

Apr 5, 2018

#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#