(1/81)^-3/4

Jasonbradley

2 min read

·

Jun 16, 2024

11

Share

Simplifying (1/81)^(-3/4)

This problem involves simplifying an expression with a fractional base and a fractional exponent. Let's break down the steps:

Understanding the Properties of Exponents

• Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent.
  • x^-n = 1/x^n
• Fractional Exponent: A fractional exponent indicates a root. The denominator of the fraction represents the type of root, and the numerator represents the power.
  • x^(m/n) = (n√x)^m

Applying the Properties to our Problem

1. Address the Negative Exponent:

   • (1/81)^(-3/4) = 1/[(1/81)^(3/4)]

2. Address the Fractional Exponent:

   • 1/[(1/81)^(3/4)] = 1/[(⁴√(1/81))^3]

3. Simplify the Root:

   • 1/[(⁴√(1/81))^3] = 1/[(1/3)^3]

4. Calculate the Power:

   • 1/[(1/3)^3] = 1/(1/27)

5. Simplify the Division:

   • 1/(1/27) = 27

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