%5E2%2F3%5E-2-simplified.jpeg "(3^5)^2/3^-2 Simplified")
Simplifying (3^5)^2 / 3^-2
This article will guide you through the process of simplifying the expression (3^5)^2 / 3^-2.
Understanding the Rules of Exponents
Before we begin, let's recall some key rules of exponents that will be useful in this simplification:
- Power of a power: (a^m)^n = a^(m*n)
- Division of powers with the same base: a^m / a^n = a^(m-n)
- Negative exponent: a^-n = 1/a^n
Simplifying the Expression
-
Apply the power of a power rule: (3^5)^2 = 3^(5*2) = 3^10
-
Apply the division of powers rule: 3^10 / 3^-2 = 3^(10-(-2)) = 3^12
-
Final result: (3^5)^2 / 3^-2 = 3^12
Conclusion
Therefore, the simplified form of (3^5)^2 / 3^-2 is 3^12. By applying the rules of exponents, we can effectively simplify complex expressions like this one.