Jasonbradley
Home

(1/27)^-4/3

2 min read Jun 16, 2024
(1/27)^-4/3

Simplifying (1/27)^(-4/3)

This problem involves simplifying an expression with a fractional exponent and a negative exponent. Here's how to break it down:

Understanding the Properties of Exponents

  • Negative Exponent: A negative exponent means taking the reciprocal of the base. For example, x⁻² = 1/x².
  • Fractional Exponent: A fractional exponent indicates a root and a power. For example, x^(m/n) = (ⁿ√x)ᵐ.

Applying the Properties

  1. Reciprocal: First, we apply the negative exponent rule: (1/27)^(-4/3) = 27^(4/3)

  2. Root and Power: Now, we apply the fractional exponent rule. The denominator of the exponent (3) indicates the cube root, and the numerator (4) indicates the fourth power: 27^(4/3) = (³√27)⁴

  3. Simplify: The cube root of 27 is 3, and then we raise that result to the fourth power: (³√27)⁴ = 3⁴ = 81

Therefore, (1/27)^(-4/3) simplifies to 81.

Related Post

Featured Posts