ANSWER
The correct choice is C.
EXPLANATION
We know that:
[tex] \sqrt[3]{7} = {7}^{ \frac{1}{3} } [/tex]
We want to simplify:
[tex]( { {7}^{ \frac{1}{3} } )}^{3} [/tex]
The exponent here is 3. This means that the base must multiply itself 3 times.
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{1}{3} } \times {7}^{ \frac{1}{3} } \times {7}^{ \frac{1}{3} } [/tex]
Recall that:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
This implies that,
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{1}{3} + \frac{1}{3} + \frac{1}{3} } [/tex]
Simplify:
[tex] ( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ \frac{3}{3}} [/tex]
[tex]( { {7}^{ \frac{1}{3} } )}^{3} = {7}^{ 1} = 7[/tex]
The correct choice is C
