## 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**

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

**Final Result**

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