To simplify the expression (x^(2/9))^(3/8), we will use the power of a power property of exponents, which states that when you raise a power to another power, you multiply the exponents.
So, we will multiply the exponents:
- Base: x
- Exponent 1: 2/9
- Exponent 2: 3/8
Now, we calculate:
x^(2/9 * 3/8)
To multiply the fractions:
2/9 * 3/8 = (2 * 3) / (9 * 8) = 6/72 = 1/12
So we have:
x^(1/12)
Thus, the simplified form of (x^(2/9))^(3/8) is x^(1/12).