(2a^2b^4)(-3a^2b^2)(5ab)

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (2a^2b^4)(-3a^2b^2)(5ab). We will use the rules of exponents to break down each step.

Understanding the Rules of Exponents

Before we begin, let's recall the key rules of exponents that will be used:

• Product of powers: a^m * a^n = a^(m+n)
• Power of a product: (ab)^n = a^n * b^n

Simplifying the Expression

1. Rearrange and group like terms: (2 * -3 * 5) * (a^2 * a^2 * a) * (b^4 * b^2 * b)

2. Apply the product of powers rule: -30 * a^(2+2+1) * b^(4+2+1)

3. Simplify the exponents: -30a^5b^7

Final Answer

Therefore, the simplified form of the expression (2a^2b^4)(-3a^2b^2)(5ab) is -30a^5b^7.