(5a^4b^2)^3

Jasonbradley

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Jun 16, 2024

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Simplifying (5a^4b^2)^3

This expression involves the power of a product and requires applying the laws of exponents. Here's how to simplify it:

Understanding the Laws of Exponents

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

Simplifying the Expression

1. Apply the power of a product rule: (5a^4b^2)^3 = 5^3 * (a^4)^3 * (b^2)^3

2. Apply the product of powers rule: 5^3 * (a^4)^3 * (b^2)^3 = 125 * a^(43) * b^(23)

3. Simplify: 125 * a^(43) * b^(23) = 125a^12b^6

Therefore, the simplified form of (5a^4b^2)^3 is 125a^12b^6.