(3n^2m^7)^3 Simplified

Jasonbradley

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Jun 16, 2024

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Simplifying (3n^2m^7)^3

This expression involves simplifying a power of a product with exponents. Here's how to break it down:

Understanding the Properties of Exponents

We'll use the following properties of exponents to simplify the expression:

• Power of a product: (ab)^n = a^n * b^n
• Power of a power: (a^m)^n = a^(m*n)

Step-by-Step Simplification

1. Apply the power of a product rule:

   (3n^2m^7)^3 = 3^3 * (n^2)^3 * (m^7)^3

2. Apply the power of a power rule:

   3^3 * (n^2)^3 * (m^7)^3 = 3^3 * n^(23) * m^(73)

3. Calculate the exponents:

   3^3 * n^(23) * m^(73) = 27n^6m^21

The Simplified Expression

Therefore, the simplified form of (3n^2m^7)^3 is 27n^6m^21.