Question

What is the product?
(3a^2b^7)(5a^3b^8)
A. 8a^5b^15
B. 8a^6b^56
C. 15a^5b^15
D. 15a^5b^56

Answer 1

Answer:

C. 15a^5b^15

Step-by-step explanation:

(3a^2b^7)(5a^3b^8)= 3*5*a^(2+3)*b^(7+8)= 15a^5b^15

Answer 2

Answer:

$\boxed{15 {a}^{5} {b}^{15} }$

Step-by-step explanation:

$Simplify \: the \: following: \\ = > 3 {a}^{2} {b}^{7} )(5 {a}^{3} {b}^{8} ) \\ \\ 3 {a}^{2} {b}^{7} \times 5 {a}^{3} {b}^{8} =3 {a}^{2 + 3} {b}^{7 + 8} \times 5 : \\ = > 3 \times 5{a}^{2 + 3} {b}^{7 + 8} \\ \\ 7+8=15: \\ = > 3 \times 5 {a}^{2 + 3} {b}^{ \boxed{15}} \\ \\ 2+3=5: \\ = > 3 \times 5 {a}^{ \boxed{5}} {b}^{15} \\ \\ 3 \times 5 =15: \\ = > \boxed{15} {a}^{5} {b}^{15}$

Additional information:

Product Rule:

${a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ {a}^{n} \times {b}^{n} = {(a \times b)}^{n}$