what is the product?\n$(3a^{2}b^{4})(-8ab^{3})\n-24ab\n-24a^{2}b^{7}\n-24a^{2}b^{12}\n-24a^{3}b^{7}$

Explanation:

Step1: Multiply coefficients

Multiply 3 and - 8. $3\times(-8)=-24$

Step2: Multiply variables with same base (a)

Use the rule $a^m\times a^n=a^{m + n}$. Here $a^2\times a=a^{2 + 1}=a^3$.

Step3: Multiply variables with same base (b)

Use the rule $b^m\times b^n=b^{m + n}$. Here $b^4\times b^3=b^{4+3}=b^7$.

Step4: Combine results

Combine the results of coefficient - multiplication and variable - multiplications. The product is $-24a^3b^7$.

Answer:

D. $-24a^3b^7$