To simplify the expression (x^(2/3))^(4/5), we can use the rule of exponents that states (a^m)^n = a^(m*n).
Applying this rule, we multiply the exponents:
- m = 2/3
- n = 4/5
So, we have:
(x^(2/3))^(4/5) = x^((2/3)*(4/5))
Next, we calculate (2/3)*(4/5):
- Multiply the numerators: 2 * 4 = 8
- Multiply the denominators: 3 * 5 = 15
This gives us:
(2/3)*(4/5) = 8/15
Putting it all together, we find:
(x^(2/3))^(4/5) = x^(8/15)
Therefore, the simplified form of the expression is x^(8/15).