Question

6-1 check your understanding: rational exponents & solving exponent problem
match each expression with its equivalent expression.
a. \\(\sqrt4{2^5}\\) b. \\(\sqrt{5}\\) c. \\(\sqrt5{2^4}\\) d. \\(\sqrt5{2}\\)
\\(2^{\frac{5}{4}}\\) \\(5^{\frac{1}{2}}\\) \\(2^{\frac{4}{5}}\\) \\(2^{\frac{1}{5}}\\)
drag each of the expressions given above into the appropriate area below, matching the expressions given in the problem statement.
a b c d

Explanation:

Step1: Convert radical to rational exponent

Recall the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$.
For A: $\sqrt[4]{2^5}=2^{\frac{5}{4}}$

Step2: Convert radical to rational exponent

For B: $\sqrt{5}=\sqrt[2]{5^1}=5^{\frac{1}{2}}$

Step3: Convert radical to rational exponent

For C: $\sqrt[5]{2^4}=2^{\frac{4}{5}}$

Step4: Convert radical to rational exponent

For D: $\sqrt[5]{2}=\sqrt[5]{2^1}=2^{\frac{1}{5}}$

Answer:

A. $2^{\frac{5}{4}}$
B. $5^{\frac{1}{2}}$
C. $2^{\frac{4}{5}}$
D. $2^{\frac{1}{5}}$