(16/81)^3/4

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (16/81)^(3/4)

This article will guide you through the process of simplifying the expression (16/81)^(3/4). We will utilize the properties of exponents and fractions to achieve this.

Understanding Fractional Exponents

A fractional exponent like (3/4) signifies both a root and a power. The denominator (4) indicates the type of root, in this case, a fourth root. The numerator (3) represents the power we raise the result to.

Applying the Properties of Exponents

1. Separate the fraction: We can rewrite the expression as: (16/81)^(3/4) = (16^(3/4)) / (81^(3/4))

2. Calculate the roots:

   • 16^(3/4): The fourth root of 16 is 2 (since 2 * 2 * 2 * 2 = 16). Then, we cube this result: 2³ = 8.
   • 81^(3/4): The fourth root of 81 is 3 (since 3 * 3 * 3 * 3 = 81). Then, we cube this result: 3³ = 27.

3. Combine the results: (16^(3/4)) / (81^(3/4)) = 8/27

Conclusion

Therefore, the simplified form of (16/81)^(3/4) is 8/27.