(6n^-5)(3n^-3)^2

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (6n^-5)(3n^-3)^2

This article aims to explain the process of simplifying the algebraic expression (6n^-5)(3n^-3)^2. We will use the properties of exponents to achieve this.

Understanding the Properties of Exponents

To simplify the expression, we need to understand the following properties of exponents:

• 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)

Simplifying the Expression

1. Simplify the exponent:

   • (3n^-3)^2 = 3^2 * (n^-3)^2 = 9n^-6

2. Apply the product of powers rule:

   • (6n^-5) * (9n^-6) = 6 * 9 * n^(-5-6)

3. Simplify the multiplication:

   • 54 * n^-11

4. Express the negative exponent in the denominator:

   • 54 / n^11

Conclusion

Therefore, the simplified form of the expression (6n^-5)(3n^-3)^2 is 54 / n^11.