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(27x^3/8y^9)^-5/3

2 min read Jun 16, 2024
(27x^3/8y^9)^-5/3

Simplifying the Expression (27x^3/8y^9)^-5/3

This article will guide you through the steps of simplifying the expression (27x^3/8y^9)^-5/3.

Understanding the Properties

Before we dive into the simplification, let's recall some essential properties of exponents:

  • Negative Exponent: a^(-n) = 1/a^n
  • Fractional Exponent: a^(m/n) = (a^m)^(1/n) = (a^(1/n))^m
  • Power of a Quotient: (a/b)^n = a^n/b^n

Simplifying the Expression

  1. Apply the Negative Exponent Property: (27x^3/8y^9)^-5/3 = 1 / (27x^3/8y^9)^(5/3)

  2. Apply the Power of a Quotient Property: 1 / (27x^3/8y^9)^(5/3) = 1 / (27^(5/3)x^(35/3) / 8^(5/3)y^(95/3))

  3. Simplify the Exponents: 1 / (27^(5/3)x^(35/3) / 8^(5/3)y^(95/3)) = 1 / (243x^5 / 32y^15)

  4. Rewrite the expression with a positive exponent: 1 / (243x^5 / 32y^15) = (32y^15) / (243x^5)

Therefore, the simplified form of (27x^3/8y^9)^-5/3 is (32y^15) / (243x^5).

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