(8/27)^4/3

Jasonbradley

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Jun 16, 2024

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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

Step-by-Step Simplification

1. Simplify the base: Find the cube root of both the numerator and the denominator:

   • ∛8 = 2
   • ∛27 = 3
   • Therefore, ∛(8/27) = 2/3

2. 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.