Question

How do you simplify `3^(1/4) * 4^(1/4)`?

Answer 1

The answer is `root(4)12`.

Because of the commutative and associative properties of multiplication, you can rewrite `a^(x)*b^(x)` as `(ab)^x`

Therefore, `3^(1/4)*4^(1/4) = 12^(1/4)`.

We also know that `a^(1/x) = root(x)a`.

Thus, `12^(1/4) = root(4)12 = root(4)(2*2*3)`.