# How do you simplify (2)^(3/6)?

Mar 23, 2018

${2}^{\frac{1}{2}} = \sqrt{2}$

#### Explanation:

Simplify the fraction in the index first.

$\frac{3}{6} = \frac{1}{2}$

${2}^{\frac{1}{2}}$ is another way of writing $\sqrt{2}$

$\sqrt{2}$ is an irrational number which cannot be calculated exactly.

Mar 23, 2018

$\sqrt{2}$

#### Explanation:

$\text{using the "color(blue)"law of exponents}$

•color(white)(x)a^(m/n)=root(n)(a^m)

$\text{simplify the exponent, that is } \frac{3}{6} = \frac{1}{2}$

$\Rightarrow {2}^{\frac{3}{6}} = {2}^{\frac{1}{2}} = \sqrt{2}$

Mar 23, 2018

$\sqrt{2}$

#### Explanation:

${2}^{\frac{3}{6}}$

You can simplify the fractional exponent just like any fraction:

$\frac{3}{6} = \frac{1}{2}$

$\therefore$

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

This can also be expressed as:

$\sqrt{2}$

We can prove this by the following:

We know that the square root of a number, when multiplied by itself equals the number. So:

${2}^{\frac{1}{2}} \times {2}^{\frac{1}{2}} = {2}^{\frac{1}{2} + \frac{1}{2}} = {2}^{1} = 2$

So:

${2}^{\frac{1}{2}}$ must be the square root of 2