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(1/8)^-4/3

2 min read Jun 16, 2024
(1/8)^-4/3

Understanding (1/8)^(-4/3)

The expression (1/8)^(-4/3) might look intimidating, but it's actually quite straightforward to simplify using basic exponent rules. Let's break it down step-by-step.

Understanding Fractional Exponents

Fractional exponents represent a combination of roots and powers. In the expression (1/8)^(-4/3), the denominator of the exponent (3) indicates a cube root, while the numerator (4) indicates a power of 4. The negative sign indicates a reciprocal.

Applying the Rules

  1. Reciprocal: A negative exponent means taking the reciprocal of the base. Therefore: (1/8)^(-4/3) = (8/1)^(4/3) = 8^(4/3)

  2. Cube Root: The denominator of the exponent (3) means taking the cube root of the base: 8^(4/3) = (∛8)^4

  3. Power: The numerator of the exponent (4) indicates raising the result to the power of 4: (∛8)^4 = 2^4

  4. Calculation: Finally, calculate 2^4: 2^4 = 16

The Solution

Therefore, (1/8)^(-4/3) simplifies to 16.

Key Takeaways

  • Fractional exponents combine roots and powers.
  • Negative exponents represent reciprocals.
  • Understanding these rules helps simplify complex expressions.

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