Question

using rational exponents to rewrite expressions - item 50627 question 2 of 7 which expression has the same meaning as (5^{\frac{4}{5}})? options: (sqrt5{8^3}), (sqrt5{8^5}), (sqrt5{5^8}), (sqrt5{5^4})

Explanation:

Step1: Recall the formula for rational exponents

The formula for converting a rational exponent to a radical is \( a^{\frac{m}{n}}=\sqrt[n]{a^{m}} \), where \( a \) is the base, \( m \) is the numerator of the exponent, and \( n \) is the denominator of the exponent.

Step2: Apply the formula to \( 5^{\frac{4}{5}} \)

Here, \( a = 5 \), \( m = 4 \), and \( n = 5 \). So, using the formula \( a^{\frac{m}{n}}=\sqrt[n]{a^{m}} \), we get \( 5^{\frac{4}{5}}=\sqrt[5]{5^{4}} \).

Answer:

\(\sqrt[5]{5^{4}}\) (the option with \(\sqrt[5]{5^{4}}\))