Question

Which is equivalent

Answer 1

`x^(2/3)`

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)`

Answer 2

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