Answer:
D
Step-by-step explanation:
1. Use property of exponents:
[tex](a^b)^c=a^b\cdot ... \cdot a^b\ [\text{ take }c \text{ times } a^b][/tex]
Hence
[tex](7^{\frac{1}{3}})^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}[/tex]
2. Use multiplication property of exponents:
[tex]a^b\cdot a^c=a^{b+c}[/tex]
Thus,
[tex]7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}[/tex]
3. Since
[tex]\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{3}=1,[/tex]
we have that
[tex]7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^1=7[/tex]
