How can we simplify the expression (x^(2/5))^(5/6)?

To simplify the expression (x^2/5)^5/6, we can use the rules of exponents, particularly the power of a power rule. This rule states that when you raise a power to another power, you multiply the exponents. Therefore:

1. First, we identify the exponents: the base is x, and we have two exponents: 2/5 and 5/6.
2. Next, we multiply the exponents: (2/5) * (5/6).
3. Performing the multiplication, we get:
• 2 * 5 = 10
• 5 * 6 = 30
4. This gives us an overall exponent of 10/30.
5. Now, we can simplify the fraction 10/30:
• Both numbers can be divided by 10li> to yield:
• 10/30 = 1/3.
6. Finally, we can express the simplified version as:

x^1/3

Thus, the simplified expression is x^1/3.