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

Jasonbradley

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Jun 16, 2024

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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.