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(27/64)^-4/3

2 min read Jun 16, 2024
(27/64)^-4/3

Simplifying (27/64)^(-4/3)

This article will guide you through simplifying the expression (27/64)^(-4/3). We will use the properties of exponents to arrive at the solution.

Understanding the Properties of Exponents

Before we begin, let's refresh our memory on a couple of key exponent properties:

  1. Negative Exponents: x^(-n) = 1/x^n
  2. Fractional Exponents: x^(m/n) = (x^m)^(1/n) = (x^(1/n))^m

Simplifying the Expression

  1. Applying the Negative Exponent Property:

    (27/64)^(-4/3) = 1 / (27/64)^(4/3)

  2. Applying the Fractional Exponent Property:

    1 / (27/64)^(4/3) = 1 / [(27/64)^(1/3)]^4

  3. Simplifying the Cube Root:

    1 / [(27/64)^(1/3)]^4 = 1 / (3/4)^4

  4. Evaluating the Power:

    1 / (3/4)^4 = 1 / (81/256)

  5. Dividing by a Fraction:

    1 / (81/256) = 256/81

Therefore, (27/64)^(-4/3) simplifies to 256/81.

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