%5E4.jpeg "(2a^3)^4")
Simplifying (2a^3)^4
In mathematics, simplifying expressions is a crucial skill. Today, we'll delve into simplifying the expression (2a^3)^4.
Understanding the Rules
The key to simplifying this expression lies in understanding 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
Let's break down the simplification step by step:
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Apply the power of a product rule: (2a^3)^4 = 2^4 * (a^3)^4
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Apply the power of a power rule: 2^4 * (a^3)^4 = 2^4 * a^(3*4)
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Simplify: 2^4 * a^(3*4) = 16a^12
Final Result
Therefore, the simplified form of (2a^3)^4 is 16a^12.
Summary
By applying the rules of exponents, we were able to simplify the expression (2a^3)^4. Remember to break down the problem into smaller steps, apply the relevant rules, and carefully perform the calculations. This approach will help you simplify any expression involving exponents with ease.