Question

Which is equivalent

Answer 1

For this case we must find an expression equivalent to:

$(x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}$

By definition of power properties we have to:

$(a ^ n) ^ m = a ^ {n * m}$

So, rewriting the expression we have:

$x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =$

$x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =$

By definition of multiplication of powers of the same base, we put the same base and add the exponents:

$x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}$

Answer:

Option B

Answer 2

Answer:

$x^{2/3}$

Step-by-step explanation:

The question is on rules of rational exponents

Here we apply the formulae for product rule where;

$= a^{n} *a^{t} = a^{n+t} \\\\\\\\=(x^{4/3} *x^{2/3} ) = x^{4/3 + 2/3} = x^{6/3} = x^{2} \\\\\\=(x^2)^{1/3} \\\\\\=\sqrt[3]{x^2}$

$=x^{2/3}$