For this case we must find an expression equivalent to:
[tex](x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, rewriting the expression we have:
[tex]x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =[/tex]
[tex]x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =[/tex]
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
[tex]x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}[/tex]
Answer:
Option B
