Question

Write 16^34 in radical form

(This reads as 16 raised to the 3/4th power)
163 (This reads as the fourth root of 16 raised to the 3rd power)
23 (This reads as 2 raised to the 3rd power)
16^4 (This reads as the cubed root of 16 raised to the 4th power)
none of the above

Answer 1

So 16^3/4 = (the fourth root of 16)^3

Explanation:

Initially, we know that 16^3/4 = 8

However, that is not what the question is asking, we need to rewrite 16^3/4 in radical form.

An important point to note is that radical form involves the use of surds, or roots.

Thus, the formula we need to use is this:

a^b/c = (the cth root of a)^b

For example:

8^2/3 = (the cube root of 8)^2

So 16^3/4 = (the fourth root of 16)^3