Question
Find the products: Multiply $-\frac{2}{3}\text{a}^2\text{b by }\frac{6}{5}\text{a}^3\text{b}^2$ and verify your result for $a = 2$ and $b = 3.$
✓
Answer
$\frac{-2}{3}\text{a}^2\text{b}\times \frac{6}{5}\text{a}^3\text{b}^2$
$=\frac{-2}{3}\times \frac{6}{5}\text{a}^2\times \text{a}^3\times \text{b}\times \text{b}^2$
$=\frac{-4}{5}\text{a}^{2+3}\text{b}^{1+2}$
$=\frac{-4}{5}\text{a}^5\text{b}^3$
Verification:
Now if $a = 2, b = 3$, then $-\frac{2}{3}\text{a}^2\text{b}=\frac{-2}{3}\times (2)^2\times 3$
$=\frac{-2}{3}\times 4\times 3$
$=-8$
$\frac{6}{5}\text{a}^3\text{b}^2=\frac{6}{5}\times (2)^3\times (3)^2$
$=\frac{6}{5}\times 2\times 2\times 2\times 3\times 3$
$=\frac{6}{5}\times 8\times 9=\frac{432}{5}$
$\therefore \text{L.H.S} = -8 \times \frac{432}{5}$
$=\frac{-3456}{5}$
$\text{R.H.S}=\frac{-4}{5}\text{a}^5\text{b}^3=\frac{-4}{5}(2)^5(3)^3$
$=\frac{-4}{5}(2\times2\times2\times2\times2)\times3\times3\times3$
$=\frac{-4}{5}\times32\times27$
$=\frac{-4\times864}{5}=\frac{-3456}{5}$
$\therefore \frac{-3456}{5}=\frac{-3456}{5}$
$\text{L.H.S.}= \text{R.H.S}$
$=\frac{-2}{3}\times \frac{6}{5}\text{a}^2\times \text{a}^3\times \text{b}\times \text{b}^2$
$=\frac{-4}{5}\text{a}^{2+3}\text{b}^{1+2}$
$=\frac{-4}{5}\text{a}^5\text{b}^3$
Verification:
Now if $a = 2, b = 3$, then $-\frac{2}{3}\text{a}^2\text{b}=\frac{-2}{3}\times (2)^2\times 3$
$=\frac{-2}{3}\times 4\times 3$
$=-8$
$\frac{6}{5}\text{a}^3\text{b}^2=\frac{6}{5}\times (2)^3\times (3)^2$
$=\frac{6}{5}\times 2\times 2\times 2\times 3\times 3$
$=\frac{6}{5}\times 8\times 9=\frac{432}{5}$
$\therefore \text{L.H.S} = -8 \times \frac{432}{5}$
$=\frac{-3456}{5}$
$\text{R.H.S}=\frac{-4}{5}\text{a}^5\text{b}^3=\frac{-4}{5}(2)^5(3)^3$
$=\frac{-4}{5}(2\times2\times2\times2\times2)\times3\times3\times3$
$=\frac{-4}{5}\times32\times27$
$=\frac{-4\times864}{5}=\frac{-3456}{5}$
$\therefore \frac{-3456}{5}=\frac{-3456}{5}$
$\text{L.H.S.}= \text{R.H.S}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Solve the following equations. Check your result in case. $\frac{2\text{x}-3}{5}+\frac{\text{x}+3}{4}=\frac{4\text{x}+1}{7}$
→A calculator has only ‘+1,000’, ‘+100’, and ‘+10’buttons. Write an expression describing the number of button clicks to be made for the following numbers :
(a) 850
(b) 2,140
(c) 10,500
(d) 7,53,020
(a) 850
(b) 2,140
(c) 10,500
(d) 7,53,020
A fruit seller earns a profit of ₹ 6 per bag of mangoes sold and a loss of ₹ 3 per bag of grapes sold.
(i) Fruit seller sells 700 bags of mangoes and 800 bags of grapes. What is his profit or loss?
(ii) If he sold 500 bags of grapes. Then to have neither profit nor loss, how many bags of mangoes, he has to sell?
(i) Fruit seller sells 700 bags of mangoes and 800 bags of grapes. What is his profit or loss?
(ii) If he sold 500 bags of grapes. Then to have neither profit nor loss, how many bags of mangoes, he has to sell?
Two cross roads, each of width $5 \ m$, run at right angles through the centre of a rectangular park of length $70 \ m$ and breadth $45 \ m$ and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of ₹ $105 ~per ~m^2$.
→Iron rods $a, b, c, d, e$ and $f$ are making a design in a bridge as shown in $Fig.$ in which $a \| b, c \| d, e \| f.$ Find the marked angles between.
$i. b$ and $c$
$ii. d$ and $e$
$iii. d$ and $f$
$iv. c$ and $f$
→$i. b$ and $c$
$ii. d$ and $e$
$iii. d$ and $f$
$iv. c$ and $f$
The area of a square and a rectangle are equal. If the side of the square is $40 \ cm$ and the breadth of the rectangle is $25 \ cm$, find the length of the rectangle. Also, find the perimeter of the rectangle.
→Find the mode of the following data :
$
\begin{array}{l}
12,14,12,16,15,13,14,18,19,12,14,15,16 \text {, } \\
15,16,16,15,17,13,16,16,15,15,13,15,17 \\
15,14,15,13,15,14
\end{array}
$
→$
\begin{array}{l}
12,14,12,16,15,13,14,18,19,12,14,15,16 \text {, } \\
15,16,16,15,17,13,16,16,15,15,13,15,17 \\
15,14,15,13,15,14
\end{array}
$
Rahul scored of 97, 73 and 80, respectively in his first three examinations. If he scored 70 in the fourth examination, then find how much average score increased/decreased?
In Fig.name each linear pair and each pair of vertically opposite angles:
$\frac{\text{5x}-1}{3}-\frac{2\text{x}-2}{3}=1$
→