(25^1/2 X^5)(4x^-6)

2 min read Jun 16, 2024
(25^1/2 X^5)(4x^-6)

Simplifying Expressions with Exponents

This article will walk through the process of simplifying the expression (25^1/2 x^5)(4x^-6).

Understanding the Properties of Exponents

Before we begin simplifying, let's recall some key properties of exponents:

  • Product of Powers: When multiplying powers with the same base, you add the exponents.
    • x^m * x^n = x^(m+n)
  • Power of a Power: When raising a power to another power, you multiply the exponents.
    • (x^m)^n = x^(m*n)
  • Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent.
    • x^-n = 1/x^n

Simplifying the Expression

  1. Simplify the numerical terms:

    • 25^(1/2) = 5 (The square root of 25 is 5)
  2. Apply the product of powers rule:

    • x^5 * x^-6 = x^(5-6) = x^-1
  3. Combine the simplified terms:

    • (5 * x^-1)(4)
    • 20x^-1
  4. Apply the negative exponent rule:

    • 20x^-1 = 20/x

Final Result

The simplified expression is 20/x.

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