%5E2.jpeg "(60x^10y^7/5x^4y^3)^2")
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^(m-n)
- Power of a power: (x^m)^n = x^(m*n)
Simplifying the Expression
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Simplify inside the parentheses:
- Divide the coefficients: 60/5 = 12
- Apply the quotient of powers rule for the x terms: x^(10-4) = x^6
- Apply the quotient of powers rule for the y terms: y^(7-3) = y^4
- This gives us: (12x^6y^4)^2
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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.