Question

which expressions are equivalent to (a^{\frac{b}{c}})?

select all correct answer choices.

((\sqrtb{a})^c)

((\sqrtc{a})^b)

(\sqrtc{a^b})

(\sqrtc{a})

(\sqrtb{a})

(\sqrtb{a^c})

Explanation:

Step1: Apply rational exponent definition

$$a^{\frac{b}{c}} = (a^{\frac{1}{c}})^{b} = (\sqrt[c]{a})^{b}$$

Step2: Apply power of radical property

$$a^{\frac{b}{c}} = (a^{b})^{\frac{1}{c}} = \sqrt[c]{a^{b}}$$

Answer:

B. \((\sqrt[c]{a})^{b}\)
C. \(\sqrt[c]{a^{b}}\)