why is 16^(1/2) equal to 4?

16^(1/2)

= $${{\mathtt{16}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}$$

= $${\left({{\mathtt{4}}}^{{\mathtt{2}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}$$

= $${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{1}}}{{\mathtt{2}}}}$$   = $${\mathtt{1}}$$

so that answer is 4

16^(1/2) is equivalent to the square root of 16 which is 4.

4*4 = 16; 16^(1/2) is the same as  $${\sqrt{{\mathtt{16}}}}$$  = 4.

If it were 16^(1/3), then we would have to take the cube root and not the square root.

That is an interesting explanation Sasini. I will give you thumbs up too.