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 the coefficients

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

Step2: Apply the rule of exponents for (a) terms ((a^m\times a^n=a^{m + n}))

For (a^2\times a=a^{2+1}=a^3)

Step3: Apply the rule of exponents for (b) terms ((b^m\times b^n=b^{m + n}))

For (b^4\times b^3=b^{4 + 3}=b^7)

Step4: Combine the results

Combine the coefficient and the variable - parts. The product is (-24\times a^3\times b^7=-24a^3b^7)

Answer:

(-24a^3b^7) (the fourth option)