(3/4)^-x^2 81/256

2 min read Jun 16, 2024
(3/4)^-x^2 81/256

Simplifying Exponential Expressions: (3/4)^-x^2 * 81/256

This article will walk you through the process of simplifying the expression (3/4)^-x^2 * 81/256. We'll utilize the properties of exponents to achieve a concise and understandable solution.

Understanding the Properties

Before diving into the simplification, let's recall some key properties of exponents:

  • Negative exponents: a^-n = 1/a^n
  • Fractional exponents: a^(m/n) = (a^m)^(1/n) = (a^(1/n))^m
  • Product of powers: a^m * a^n = a^(m+n)

Simplifying the Expression

  1. Address the negative exponent: (3/4)^-x^2 = 1 / (3/4)^x^2

  2. Rewrite the fraction 81/256 in terms of 3/4: 81/256 = (3^4) / (4^4) = (3/4)^4

  3. Combine the terms: 1 / (3/4)^x^2 * (3/4)^4 = (3/4)^4 / (3/4)^x^2

  4. Apply the product of powers rule: (3/4)^4 / (3/4)^x^2 = (3/4)^(4 - x^2)

Final Result

The simplified expression is (3/4)^(4 - x^2).

Conclusion

By applying the fundamental properties of exponents, we were able to simplify the expression into a more manageable form. This approach can be applied to various similar expressions involving negative exponents and fractions.

Related Post


Featured Posts