(3d^-4)(5d^8)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (3d^-4)(5d^8)

This article will walk you through the steps of simplifying the algebraic expression (3d^-4)(5d^8).

Understanding the Rules

To simplify this expression, we'll utilize the following rules of exponents:

• Product of powers: When multiplying exponents with the same base, you add the powers.
  • Example: x^m * x^n = x^(m+n)
• Negative exponents: A term with a negative exponent in the numerator can be rewritten with a positive exponent in the denominator.
  • Example: x^-n = 1/x^n

Simplifying the Expression

1. Rearrange the terms:
   (3d^-4)(5d^8) = (3 * 5)(d^-4 * d^8)

2. Apply the product of powers rule: (3 * 5)(d^-4 * d^8) = 15d^(-4+8)

3. Simplify the exponents: 15d^(-4+8) = 15d^4

Final Answer

The simplified form of the expression (3d^-4)(5d^8) is 15d^4.