question
express $8^{\frac{1}{5}}$ in simplest radical form.
answer attempt 4 out of 4

Question

Accepted Answer

# Explanation:
## Step1: Recall the exponent rule $ a^{\frac{m}{n}}=\sqrt[n]{a^m} $ (when $ n>0 $). For $ 8^{\frac{1}{5}} $, here $ a = 8 $, $ m = 1 $, $ n = 5 $.
So by the rule, $ 8^{\frac{1}{5}}=\sqrt[5]{8^1} $
## Step2: Simplify $ 8^1 $ which is just 8. So we have $ \sqrt[5]{8} $. Since 8 cannot be simplified further under a fifth - root (as 8 does not have any perfect fifth - power factors other than 1), this is the simplest radical form.
# Answer:
$\sqrt[5]{8}$

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Question

Explanation:

Step1: Recall the exponent rule \( a^{\frac{m}{n}}=\sqrt[n]{a^m} \) (when \( n>0 \)). For \( 8^{\frac{1}{5}} \), here \( a = 8 \), \( m = 1 \), \( n = 5 \).

Step2: Simplify \( 8^1 \) which is just 8. So we have \( \sqrt[5]{8} \). Since 8 cannot be simplified further under a fifth - root (as 8 does not have any perfect fifth - power factors other than 1), this is the simplest radical form.

Answer: