RD Sharma solution class 8 chapter 8 Division of Algebraic Expression Exercise 8.2

Exercise 8.2

Page-8.4

Question 1:

Divide 6x³y²z² by 3x²yz.

Answer 1:

$\frac{6x^3{y}^2{z}^2}{3x^{2}yz}=\frac{6\times x\times x\times x\times y\times y\times z\times z}{3\times x\times x\times y\times z} = 2x^{(3-2)}{y}^{(2-1)}{z}^{(2-1)}=2xyz$

Question 2:

Divide 15m²n³ by 5m²n².

Answer 2:

$$\begin{gathered} \frac{15m^2{n}^3}{5m^2{n}^2} \\ =\frac{15\times m\times m\times n\times n\times n}{5\times m\times m\times n\times n} \\ =3m^{(2-2)}{n}^{(3-2)} \\ =3m^0{n}^1 \\ =3n \end{gathered}$$

Question 3:

Divide 24a³b³ by −8ab.

Answer 3:

$$\begin{gathered} \frac{24a^3{b}^3}{-8ab} \\ = \frac{24\times a\times a\times a\times b\times b\times b}{-8\times a\times b} \\ =-3a^{(3-1)}{b}^{(3-1)} \\ =-3a^2{b}^2 \end{gathered}$$

Question 4:

Divide −21abc² by 7abc.

Answer 4:

$$\begin{gathered} \frac{-21ab{c}^2}{7abc} \\ = \frac{-21\times a\times b\times c\times c}{7\times a\times b\times c} \\ =-3a^{(1-1)}{b}^{(1-1)}{c}^{(2-1)} \\ =-3c \end{gathered}$$

Question 5:

Divide 72xyz² by −9xz.

Answer 5:

​$$\begin{gathered} \frac{72xy{z}^2}{-9xz} \\ =\frac{72\times x\times y\times z\times z}{-9\times x\times z} \\ =-8x^{(1-1)}y{z}^{(2-1)} \\ =-8yz \end{gathered}$$

Question 6:

Divide −72a⁴b⁵c⁸ by −9a²b²c³.

Answer 6:

$$\begin{gathered} \frac{-72a^4{b}^5{c}^8}{-9a^2{b}^2{c}^3} \\ =\frac{-72\times a\times a\times a\times a\times b\times b\times b\times b\times b\times c\times c\times c\times c\times c\times c\times c\times c}{-9\times a\times a\times b\times b\times c\times c\times c} \\ =8a^{(4-2)}{b}^{(5-2)}{c}^{(8-3)} \\ =8a^2{b}^3{c}^5 \end{gathered}$$

Question 7:

Simplify:
$\frac{16m^3{y}^2}{4m^{2}y}$

Answer 7:

$$\begin{gathered} \frac{16m^3{y}^2}{4m^{2}y} \\ =\frac{16\times m\times m\times m\times y\times y}{4\times m\times m\times y} \\ =4m^{(3-2)}{y}^{(2-1)} \\ =4my \end{gathered}$$

Question 8:

Simplify:
$\frac{32m^2{n}^3{p}^2}{4mnp}$

Answer 8:

$$\begin{gathered} \frac{32m^2{n}^3{p}^2}{4mnp} \\ =\frac{32\times m\times m\times n\times n\times n\times p\times p}{4\times m\times n\times p} \\ =8m^{(2-1)}{n}^{(3-1)}{p}^{(2-1)} \\ =8m{n}^{2}p \end{gathered}$$