(5x^3)(-3x^-2) Simplified

Jasonbradley

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Jun 16, 2024

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Simplifying (5x^3)(-3x^-2)

This expression involves multiplying two terms with exponents. Let's break down the simplification process step-by-step.

Understanding the Properties of Exponents

• Multiplication of powers with the same base: When multiplying powers with the same base, we add the exponents.
  • 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, and vice versa.
  • Example: x^-n = 1/x^n

Simplifying the Expression

1. Multiply the coefficients: (5)(-3) = -15
2. Apply the rule for multiplying powers with the same base: x^3 * x^-2 = x^(3+(-2)) = x^1
3. Simplify x^1: x^1 = x

Final Result

Therefore, the simplified form of (5x^3)(-3x^-2) is -15x.