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

`\boxed{15 {a}^(5) {b}^(15) }`

Explanation:

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

Additional information:

Product Rule:

`{a}^(m) * {a}^(n) = {a}^(m + n) \\ \\ {a}^(n) * {b}^(n) = {(a * b)}^(n)`

Answer 2

C. 15a^5b^15

Explanation:

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