To simplify \( 3^{1/4} \) and \( 27^{1/4} \), let’s tackle each term separately.
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Simplifying \( 3^{1/4} \):
- This term is already in its simplest form.
So, \( 3^{1/4} \) remains \( 3^{1/4} \).
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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 \( 3^{3/4} \).