Question

which radical expressions are equivalent to (7^{\frac{5}{4}})?

select all correct answer choices.

(sqrt5{7})

((sqrt4{7})^{5})

(sqrt5{7^{4}})

((sqrt5{7})^{4})

(sqrt4{7^{5}})

(sqrt{7})

Explanation:

Step1: Apply rational exponent definition

$$a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$$

Step2: Identify parameters

$$a = 7, \quad m = 5, \quad n = 4$$

Step3: Rewrite the expression

$$7^{\frac{5}{4}} = \sqrt[4]{7^5} = (\sqrt[4]{7})^5$$

Answer:

B. \((\sqrt[4]{7})^5\)
E. \(\sqrt[4]{7^5}\)