# How do you express sqrtt as a fractional exponent?

Apr 5, 2018

${t}^{\frac{1}{2}}$

#### Explanation:

$\sqrt{t}$

is actually

${2}_{\sqrt{t}}$

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

${t}^{\frac{1}{2}}$

Apr 5, 2018

${t}^{\frac{1}{2}}$

#### Explanation:

When taking the square root of something you raise its power to $\frac{1}{2}$. 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:

$\sqrt{t} \times \sqrt{t} = t$

And from the Laws of exponents, we know that the sum of the two exponents should equal 1. In the case of
$\sqrt{t} \times \sqrt{t}$ this is equal to $t$, which is essentially ${t}^{1}$.

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

${t}^{x} \times {t}^{x} = {t}^{1}$

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

$x + x = 1$
$x = \left(\frac{1}{2}\right)$

Therefore we can conclude that:
${t}^{\frac{1}{2}} = \sqrt{t}$