Jasonbradley
Home

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

less than a minute read Jun 17, 2024
(x^-3)^4x^4/2x^-3

Simplifying Exponential Expressions

Let's break down the simplification of the expression (x^-3)^4x^4/2x^-3.

Understanding the Properties

Before diving in, let's recall some essential properties of exponents:

  • Power of a power: (x^m)^n = x^(m*n)
  • Product of powers: x^m * x^n = x^(m+n)
  • Quotient of powers: x^m / x^n = x^(m-n)

Applying the Properties

  1. Simplify the numerator:

    • (x^-3)^4 = x^(-3*4) = x^-12
    • x^-12 * x^4 = x^(-12+4) = x^-8
    • Therefore, the numerator simplifies to x^-8

  2. Simplify the denominator:

    • 2x^-3 can remain as it is.

  3. Combine the numerator and denominator:

    • x^-8 / 2x^-3 = (1/2) * x^(-8 - (-3)) = (1/2) * x^-5

Final Result

The simplified expression is (1/2)x^-5. This can also be written as 1/(2x^5).

Featured Posts