Simplify (12x^3y^3)(6x^4y^6)

Problem

(12*x3*y3)*(6*x4*y6)

Solution

1. Group the coefficients and the variables with the same bases together.

12⋅6⋅x3⋅x4⋅y3⋅y6

2. Multiply the numerical coefficients to find the new constant.

12⋅6=72

3. Apply the product rule for exponents, which states am⋅an=a(m+n) to the x terms.

x3⋅x4=x(3+4)=x7

4. Apply the product rule for exponents to the y terms.

y3⋅y6=y(3+6)=y9

5. Combine the results into a single simplified expression.

72*x7*y9

Final Answer

(12*x3*y3)*(6*x4*y6)=72*x7*y9

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