Question

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

Answer 1

`2^(1/2) = sqrt2`

Explanation:

Simplify the fraction in the index first.

`3/6 = 1/2`

`2^(1/2)` is another way of writing `sqrt2`

`sqrt2` is an irrational number which cannot be calculated exactly.

Answer 2

`sqrt2`

Explanation:

`"using the "color(blue)"law of exponents"`

`•color(white)(x)a^(m/n)=root(n)(a^m)`

`"simplify the exponent, that is "3/6=1/2`

`rArr2^(3/6)=2^(1/2)=sqrt2`

Answer 3

`sqrt(2)`

Explanation:

`2^(3/6)`

You can simplify the fractional exponent just like any fraction:

`3/6=1/2`

`:.`

`2^(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^(1/2)xx2^(1/2)=2^(1/2+1/2)=2^1=2`

So:

`2^(1/2)` must be the square root of 2