%5E2-%2F-3%5E-2.jpeg "(3^5)^2 / 3^-2")
Simplifying Exponential Expressions: (3^5)^2 / 3^-2
This article will explore the simplification of the expression (3^5)^2 / 3^-2 using the rules of exponents.
Understanding the Rules of Exponents
Before we begin, let's recall the key rules of exponents that we will use:
- Power of a power: (a^m)^n = a^(m*n)
- Division of exponents: a^m / a^n = a^(m-n)
- Negative exponent: a^-n = 1/a^n
Simplifying the Expression
Let's break down the expression step-by-step:
- Apply the power of a power rule: (3^5)^2 = 3^(5*2) = 3^10
- Apply the negative exponent rule: 3^-2 = 1/3^2
- Substitute the simplified terms back into the original expression: 3^10 / (1/3^2)
- Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, 3^10 / (1/3^2) = 3^10 * 3^2
- Apply the division of exponents rule: 3^10 * 3^2 = 3^(10+2) = 3^12
Final Result
Therefore, the simplified expression of (3^5)^2 / 3^-2 is 3^12.