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

Problem

(2*u2*v3)3*(3*u(−3)*v)2

Solution

1. Apply the power of a product rule to the first term by raising each factor inside the parentheses to the third power.

(2*u2*v3)3=2⋅(u2)3⋅(v3)3

2⋅(u2)3⋅(v3)3=8*u6*v9

2. Apply the power of a product rule to the second term by raising each factor inside the parentheses to the second power.

(3*u(−3)*v)2=3⋅(u(−3))2⋅v2

3⋅(u(−3))2⋅v2=9*u(−6)*v2

3. Multiply the coefficients and the variables together using the product rule for exponents.

8⋅9⋅u6⋅u(−6)⋅v9⋅v2

4. Simplify the exponents by adding them for like bases.

72*u(6−6)*v(9+2)

72*u0*v11

5. Apply the zero exponent rule where u0=1

72⋅1⋅v11

72*v11

Final Answer

(2*u2*v3)3*(3*u(−3)*v)2=72*v11

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