Simplify.

3^1/4
27^1/4

1 answer

To simplify \( 3^{1/4} \) and \( 27^{1/4} \), let’s tackle each term separately.

  1. Simplifying \( 3^{1/4} \):

    • This term is already in its simplest form.

    So, \( 3^{1/4} \) remains \( 3^{1/4} \).

  2. Simplifying \( 27^{1/4} \):

    • First, we can rewrite 27 as a power of 3: \( 27 = 3^3 \).
    • Therefore, we have: \[ 27^{1/4} = (3^3)^{1/4} \]
    • Using the power of a power property (i.e., \( (a^m)^n = a^{mn} \)): \[ (3^3)^{1/4} = 3^{3/4} \]

Now we can summarize the results:

  • \( 3^{1/4} \) is simply \( 3^{1/4} \).
  • \( 27^{1/4} \) simplifies to \( 3^{3/4} \).

Thus the two terms are:

  • \( 3^{1/4} \)
  • \( 3^{3/4} \)

If you want to combine them, they are already in a unique form, and can be presented as is:

  • \( 3^{1/4} \) and \( 3^{3/4} \).