Answer:
(D)[tex](7^{\frac{1}{3}})^3=7[/tex]
Step-by-step explanation:
The following statement is:
[tex]\sqrt[3]{7}=7^{\frac{1}{3}}[/tex]
Now, [tex](7^{\frac{1}{3}})^3=7^{\frac{1}{3}}\cdot7^{\frac{1}{3}}\cdot7^{\frac{1}{3}}[/tex]
Using, the power and exponents properties that is [tex]a^a{\cdot}a^b=a^{a+b}[/tex], we get
[tex](7^{\frac{1}{3}})^3=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}[/tex]
[tex](7^{\frac{1}{3}})^3=7^{\frac{3}{3}}[/tex]
[tex](7^{\frac{1}{3}})^3=7^1[/tex]
[tex](7^{\frac{1}{3}})^3=7[/tex]
Thus, option D is correct.
