%5E4.jpeg "(2a^3a^2)^4")
Simplifying the Expression: (2a^3a^2)^4
This article will guide you through simplifying the expression (2a^3a^2)^4. We'll use the rules of exponents to break it down step-by-step.
Understanding the Rules of Exponents
Before we begin, let's recall some key rules of exponents:
- Product of Powers: a^m * a^n = a^(m+n)
- Power of a Product: (ab)^n = a^n * b^n
- Power of a Power: (a^m)^n = a^(m*n)
Simplifying the Expression
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Combine terms inside the parentheses: (2a^3a^2) = 2a^(3+2) = 2a^5
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Apply the Power of a Product rule: (2a^5)^4 = 2^4 * (a^5)^4
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Apply the Power of a Power rule: 2^4 * (a^5)^4 = 16 * a^(5*4) = 16a^20
Final Result
Therefore, the simplified expression of (2a^3a^2)^4 is 16a^20.