Simplify (3xy^3)^2(xy)^6

Problem

(3*x*y^3)^2*(x*y)^6

Solution

1. Apply the power of a product rule to the first term (3*x*y^3)^2 by squaring each factor inside the parentheses.

(3*x*y^3)^2=3^2⋅x^2⋅(y^3)^2

2. Simplify the exponents in the first term using the power of a power rule (a^m)^n=a^(m*n)

3^2⋅x^2⋅(y^3)^2=9*x^2*y^6

3. Apply the power of a product rule to the second term (x*y)^6

(x*y)^6=x^6*y^6

4. Multiply the expressions together by combining the results from the previous steps.

9*x^2*y^6⋅x^6*y^6

5. Combine like bases using the product rule for exponents a^m⋅a^n=a^(m+n)

9⋅x^(2+6)⋅y^(6+6)

6. Simplify the final exponents to reach the result.

9*x^8*y^12

Final Answer

(3*x*y^3)^2*(x*y)^6=9*x^8*y^12

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