Simplify (3u^3v^3)^2(2u^-2v)^3

Problem

(3*u3*v3)2*(2*u(−2)*v)3

Solution

1. Apply the power of a product rule to the first term (3*u3*v3)2 by squaring each factor inside the parentheses.

3*(u3)2*(v3)2

9*u6*v6

2. Apply the power of a product rule to the second term (2*u(−2)*v)3 by cubing each factor inside the parentheses.

2*(u(−2))3*(v1)3

8*u(−6)*v3

3. Multiply the coefficients together.

9⋅8=72

4. Multiply the variables by adding the exponents of terms with the same base.

u6⋅u(−6)=u(6+(−6))=u0=1

v6⋅v3=v(6+3)=v9

5. Combine the results to find the final simplified expression.

72⋅1⋅v9=72*v9

Final Answer

(3*u3*v3)2*(2*u(−2)*v)3=72*v9

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