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(27/8)^2/3

2 min read Jun 16, 2024
(27/8)^2/3

Calculating (27/8)^(2/3)

This article will guide you through calculating the expression (27/8)^(2/3).

Understanding Fractional Exponents

A fractional exponent like (2/3) represents both a root and a power. In this case:

  • The denominator (3) indicates the type of root: It's a cube root, meaning we need to find a number that, when multiplied by itself three times, gives us the original number.
  • The numerator (2) indicates the power: We need to raise the result to the power of 2.

Step-by-Step Calculation

  1. Cube Root of 27/8:
    The cube root of 27 is 3 (3 x 3 x 3 = 27). The cube root of 8 is 2 (2 x 2 x 2 = 8). Therefore, the cube root of (27/8) is (3/2).

  2. Squaring the Result: Now, we need to square the result from step 1: (3/2)^2 = (3/2) * (3/2) = 9/4.

Final Result

Therefore, (27/8)^(2/3) is equal to 9/4.

Key Points to Remember

  • Fractional exponents represent both roots and powers.
  • The denominator indicates the type of root, and the numerator indicates the power.
  • You can break down the calculation into smaller steps for easier understanding.

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