%5E3-simplify.jpeg "(3x^2)^3 Simplify")
Simplifying (3x^2)^3
In mathematics, simplifying expressions is a crucial step in solving equations and understanding mathematical concepts. This article will guide you through the process of simplifying the expression (3x^2)^3.
Understanding the Rules
The key to simplifying this expression lies in understanding the rules of exponents. Here's a breakdown:
- 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 apply these rules to our expression (3x^2)^3:
- Power of a product: We can rewrite (3x^2)^3 as 3^3 * (x^2)^3.
- Power of a power: We can further simplify (x^2)^3 to x^(2*3) = x^6.
Final Result
Therefore, the simplified expression is:
3^3 * x^6 = 27x^6
Conclusion
By applying the rules of exponents, we have successfully simplified the expression (3x^2)^3 to 27x^6. Remember to always prioritize understanding the underlying principles to navigate complex mathematical expressions with confidence.