Simplifying (xy^6)^2
In mathematics, simplifying expressions often involves applying rules of exponents. Let's break down how to simplify the expression (xy^6)^2.
Understanding the Rules
 Power of a product: (ab)^n = a^n * b^n
 Power of a power: (a^m)^n = a^(m*n)
Applying the Rules

Distribute the exponent: Using the power of a product rule, we can distribute the exponent '2' to both 'x' and 'y^6': (xy^6)^2 = x^2 * (y^6)^2

Simplify the power of a power: Applying the power of a power rule, we multiply the exponents of 'y': x^2 * (y^6)^2 = x^2 * y^(6*2) = x^2 * y^12

Rewrite with positive exponents: We can rewrite y^12 with a positive exponent by moving it to the denominator: x^2 * y^12 = x^2 / y^12
Final Result
Therefore, the simplified form of (xy^6)^2 is x^2 / y^12.