(-10n)^2(-4n^3)^3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-10n)^2(-4n^3)^3

This article will guide you through the process of simplifying the algebraic expression (-10n)^2(-4n^3)^3.

Understanding the Rules

Before we begin, let's recall some key exponent rules:

• Product of Powers: (x^m)(x^n) = x^(m+n)
• Power of a Product: (xy)^n = x^n * y^n
• Power of a Power: (x^m)^n = x^(m*n)

Step-by-Step Simplification

1. Simplify the exponents:

   • (-10n)^2 = (-10)^2 * n^2 = 100n^2
   • (-4n^3)^3 = (-4)^3 * (n^3)^3 = -64n^9

2. Combine the results:

   • 100n^2 * -64n^9 = -6400n^(2+9)

3. Simplify the final expression:

   • -6400n^(2+9) = -6400n^11

Conclusion

Therefore, the simplified form of the expression (-10n)^2(-4n^3)^3 is -6400n^11. By applying the exponent rules, we have successfully reduced the expression to a single term with a coefficient and a variable raised to a power.