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(16/81)^3/4 As A Fraction

less than a minute read Jun 16, 2024
(16/81)^3/4 As A Fraction

Simplifying (16/81)^(3/4) as a Fraction

This problem involves simplifying a fractional exponent. Let's break down the steps:

Understanding Fractional Exponents

A fractional exponent like (3/4) represents both a root and a power:

  • The denominator (4) indicates the root: In this case, it's the fourth root.
  • The numerator (3) indicates the power: Here, we need to raise the base to the power of 3.

Applying the Concepts

  1. Find the fourth root of the numerator and denominator:

    • The fourth root of 16 is 2 (since 2 * 2 * 2 * 2 = 16).
    • The fourth root of 81 is 3 (since 3 * 3 * 3 * 3 = 81).

  2. Cube the resulting numerator and denominator:

    • 2 cubed (2 * 2 * 2) is 8.
    • 3 cubed (3 * 3 * 3) is 27.

Solution

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

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