%5E3.jpeg "(4m^5n^2/m^2n)^3")
Simplifying the Expression (4m^5n^2/m^2n)^3
This article will guide you through the process of simplifying the expression (4m^5n^2/m^2n)^3.
Understanding the Properties
Before we dive into the simplification, let's review some key properties of exponents:
- Product of powers: x^m * x^n = x^(m+n)
- Quotient of powers: x^m / x^n = x^(m-n)
- Power of a power: (x^m)^n = x^(m*n)
- Power of a product: (xy)^n = x^n * y^n
- Power of a quotient: (x/y)^n = x^n / y^n
Step-by-Step Simplification
-
Simplify inside the parentheses:
- Apply the quotient of powers rule: 4m^5n^2 / m^2n = 4m^(5-2)n^(2-1) = 4m^3n
-
Apply the power of a power rule:
- (4m^3n)^3 = 4^3 * (m^3)^3 * n^3
-
Simplify:
- 4^3 * (m^3)^3 * n^3 = 64m^9n^3
Final Result
Therefore, the simplified form of the expression (4m^5n^2/m^2n)^3 is 64m^9n^3.