Question

Multiply: (a) $\left(5y^7\right)\left(-7y^4\right)$ (b) $\left(\frac{2}{5}{a}^4{b}^3\right)\left(15a{b}^3\right)$.

Short answer

Result is

(a)$-35y^{11}$

(b)$6a^5{b}^6$

Step-by-step solution

part (a) Step 1 Given information  

$\left(5y^7\right)\left(-7y^4\right)$

part (a) Step 2 

$$\begin{gathered} \left(5y^7\right)\left(-7y^4\right)=5\times -7\times y^{7+4} \\ =-35y^{11} \end{gathered}$$

part (b) Step 1 Given information  

$\left(\frac{2}{5}{a}^4{b}^3\right)\left(15a{b}^3\right)$

part (b) Step 2 

$$\begin{gathered} \left(\frac{2}{5}{a}^4{b}^3\right)\left(15a{b}^3\right)=\frac{2}{5}\times 15\times a^{4+1}\times b^{3+3} \\ =6a^5{b}^6 \end{gathered}$$