Question

Directions:Use the product rule to simplify the following monomials.

Answer 1

Question :

❖ Use the product rule to simplify the following monomials.

$\\ \tt \: 19. \: ( - 15x {y}^{4} ). \bigg( - \frac{1}{3} x {y}^{3} \bigg) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \tt\bigg[( - 15) \times \bigg( - \frac{1}{3} \bigg) \bigg] {x}^{(1 + 1)} . {y}^{(4 + 3)} \\ \\ \tt = 5 {x}^{2} {y}^{7 \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\\ \tt20. \: \: \tt ( 5 {a}^{2} {bc}^{3} ). \bigg( \frac{1}{5} a {bc}^{4} \bigg) \tt \: \: \: \: \: \: \: \: \: \: \\ \\ = \tt\bigg[5 \times \frac{1}{5} \bigg] {a}^{(2 + 1)} . {b}^{(1 + 1)} . {c}^{(3 + 4)} \\ \\ \tt = {a}^{3} {b}^{2} {c}^{7 \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\\ \tt \:21. \: \: \frac{1}{3} (2a³b)(6b³) \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt = \frac{1}{3} \times (2 \times 6) {a}^{3} . {b}^{(1 + 3)} \\ \\ \tt = \frac{1} { \cancel{3}} \times \cancel{ 12} \: ({a}^{3} {b}^{4}) \: \: \: \\ \\ \tt = 4{a}^{3} {b}^{4} \: \: \: \: \: \: \: \: \: \:$

Answer 2

Answer:

19. 5x²y⁷

20. a³b²c⁷

21. 4a³b⁴

Step-by-step explanation:

hope i helped! good luck in class!!