Simplifying the Expression (8/27)^(4/3)
In mathematics, expressions involving fractional exponents can be simplified using the properties of exponents. Let's break down how to simplify the expression (8/27)^(4/3).
Understanding Fractional Exponents
A fractional exponent like 4/3 represents both a root and a power. The denominator (3 in this case) indicates the type of root to take, which is a cube root in this example. The numerator (4) indicates the power to raise the result to.
Therefore, (8/27)^(4/3) can be interpreted as:
 Taking the cube root of (8/27): ∛(8/27) = 2/3
 Raising the result to the power of 4: (2/3)^4 = 16/81
StepbyStep Simplification

Simplify the base: Find the cube root of both the numerator and the denominator:
 ∛8 = 2
 ∛27 = 3
 Therefore, ∛(8/27) = 2/3

Raise the simplified base to the power of 4:
 (2/3)^4 = (2/3) * (2/3) * (2/3) * (2/3) = 16/81
Final Result
Therefore, (8/27)^(4/3) simplifies to 16/81.