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

Problem

(3*x*y3)2*(x*y)6

Solution

1. Apply the power of a product rule to the first term (3*x*y3)2 by squaring each factor inside the parentheses.

(3*x*y3)2=3⋅x2⋅(y3)2

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

3⋅x2⋅(y3)2=9*x2*y6

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

(x*y)6=x6*y6

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

9*x2*y6⋅x6*y6

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

9⋅x(2+6)⋅y(6+6)

6. Simplify the final exponents to reach the result.

9*x8*y12

Final Answer

(3*x*y3)2*(x*y)6=9*x8*y12

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