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

Problem

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

Solution

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

12⋅6⋅x^3⋅x^4⋅y^3⋅y^6

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

12⋅6=72

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

x^3⋅x^4=x^(3+4)=x^7

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

y^3⋅y^6=y^(3+6)=y^9

5. Combine the results into a single simplified expression.

72*x^7*y^9

Final Answer

(12*x^3*y^3)*(6*x^4*y^6)=72*x^7*y^9

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