%5E3.jpeg "(2a^2b^3)^3")
Simplifying the Expression: (2a²b³)^3
In mathematics, simplifying expressions is a fundamental skill. Let's break down how to simplify the expression (2a²b³)^3.
Understanding the Rules
To simplify this expression, we need to use the following rules of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Rules
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Apply the power of a product rule: (2a²b³)^3 = 2^3 * (a²)³ * (b³)^3
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Apply the power of a power rule to the variables: 2^3 * (a²)³ * (b³)^3 = 2^3 * a^(23) * b^(33)
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Simplify the exponents: 2^3 * a^(23) * b^(33) = 8a^6b^9
Final Result
Therefore, the simplified form of (2a²b³)^3 is 8a^6b^9.