%5E5.jpeg "(4a^2b^3)^5")
Simplifying Expressions with Exponents: (4a^2b^3)^5
In mathematics, simplifying expressions is a fundamental skill. This involves applying various rules and properties to rewrite an expression in a more concise and manageable form. One common task is simplifying expressions with exponents. Let's explore how to simplify the expression (4a^2b^3)^5.
Understanding the Rules
Before diving into the simplification process, let's recall some key rules of exponents:
- Product of Powers: x^m * x^n = x^(m+n)
- Power of a Power: (x^m)^n = x^(m*n)
- Power of a Product: (x*y)^n = x^n * y^n
Step-by-Step Simplification
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Apply the Power of a Product rule: (4a^2b^3)^5 = 4^5 * (a^2)^5 * (b^3)^5
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Apply the Power of a Power rule: 4^5 * (a^2)^5 * (b^3)^5 = 4^5 * a^(25) * b^(35)
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Simplify the exponents: 4^5 * a^(25) * b^(35) = 1024 * a^10 * b^15
Final Result
Therefore, the simplified form of (4a^2b^3)^5 is 1024a^10b^15.
Key Takeaways
- Remember to apply the rules of exponents carefully.
- Simplifying expressions can make calculations easier and improve understanding of mathematical relationships.
- Practice working with exponents to develop fluency and confidence.