Simplifying the Expression: (60x^10y^7/5x^4y^3)^2
This article will guide you through the process of simplifying the expression (60x^10y^7/5x^4y^3)^2.
Understanding the Properties of Exponents
Before we begin, let's refresh our understanding of some key exponent properties:
 Product of powers: x^m * x^n = x^(m+n)
 Quotient of powers: x^m / x^n = x^(mn)
 Power of a power: (x^m)^n = x^(m*n)
Simplifying the Expression

Simplify inside the parentheses:
 Divide the coefficients: 60/5 = 12
 Apply the quotient of powers rule for the x terms: x^(104) = x^6
 Apply the quotient of powers rule for the y terms: y^(73) = y^4
 This gives us: (12x^6y^4)^2

Apply the power of a power rule:
 (12x^6y^4)^2 = 12^2 * (x^6)^2 * (y^4)^2
 Simplify: 144x^12y^8
Final Answer
Therefore, the simplified form of the expression (60x^10y^7/5x^4y^3)^2 is 144x^12y^8.