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(8/27)^4/3 As A Fraction

2 min read Jun 16, 2024
(8/27)^4/3 As A Fraction

Simplifying (8/27)^(4/3) as a Fraction

This problem involves working with fractional exponents and simplifying expressions with fractions. Here's a step-by-step breakdown:

Understanding Fractional Exponents

A fractional exponent like 4/3 can be understood as a combination of two operations:

  • The denominator (3): Indicates taking the cube root.
  • The numerator (4): Indicates raising the result to the power of 4.

Simplifying the Expression

  1. Cube Root: Find the cube root of both the numerator and denominator of the fraction (8/27).

    • The cube root of 8 is 2 (2 x 2 x 2 = 8)
    • The cube root of 27 is 3 (3 x 3 x 3 = 27)

  2. Raise to the Power: Now, raise both the numerator and denominator to the power of 4.

    • 2^4 = 16
    • 3^4 = 81

  3. Final Result: The simplified expression is 16/81.

Therefore, (8/27)^(4/3) is equal to 16/81.

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