Question
Find product: $\Big(\frac{−2}{7}\text{a}^4\Big)×\Big(\frac{−3}{4}\text{a}^2\text{b}\Big)×\Big(\frac{−14}{5}\text{b}^2\Big)$
✓
Answer
To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, $a^m \times a^n=a^{m+n}$.
We have:
$\Big(\frac{−2}{7}\text{a}^4\Big)×\Big(\frac{−3}{4}\text{a}^2\text{b}\Big)×\Big(\frac{−14}{5}\text{b}^2\Big)$
$=\Big[\big(\frac{−2}{7}\big)×\big(\frac{−3}{4}\big)×\big(\frac{−14}{5}\big)\Big]×(\text{a}^4×\text{a}^2)×(\text{b}×\text{b}^2)$
$=−\Big(\frac{2}{7}×\frac{3}{4}×\frac{14}{5}\Big)×\text{a}^{4+2}×\text{b}^{1+2}$
$=−\frac{3}{5}\text{a}^6\text{b}^3$
Thus, the answer is $=−\frac{3}{5}\text{a}^6\text{b}^3$
We have:
$\Big(\frac{−2}{7}\text{a}^4\Big)×\Big(\frac{−3}{4}\text{a}^2\text{b}\Big)×\Big(\frac{−14}{5}\text{b}^2\Big)$
$=\Big[\big(\frac{−2}{7}\big)×\big(\frac{−3}{4}\big)×\big(\frac{−14}{5}\big)\Big]×(\text{a}^4×\text{a}^2)×(\text{b}×\text{b}^2)$
$=−\Big(\frac{2}{7}×\frac{3}{4}×\frac{14}{5}\Big)×\text{a}^{4+2}×\text{b}^{1+2}$
$=−\frac{3}{5}\text{a}^6\text{b}^3$
Thus, the answer is $=−\frac{3}{5}\text{a}^6\text{b}^3$
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: $\frac{7\text{y}}{5}=\text{y}-4$
→The rainfall recorded on a certain day was $5\ cm$. Find the volume of water that fell on a $2$-hectare field.
→Add the following rational number: $\frac{-7}{27}$ and $\frac{11}{18}$
→The surface area of a cube is $1176cm^2$. Find its volume.
→Solve the linear equation $\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}$.
→Magic Game Board
A magic game board is an array of numbers having the same number of row and columns arranged, so that the sum of the numbers in each row and column is the same.
Complete the magic game board below.
A magic game board is an array of numbers having the same number of row and columns arranged, so that the sum of the numbers in each row and column is the same.
Complete the magic game board below.
If $a$ and $b$ are any two integers, is $(a+b)^2$ always greater than $a^2+b^2$ ? If not, when is it greater?
→For the development of basic infrastructure in a district, a project of Rs $108$ crore approved by Development Bank is as follows:
Draw a pie chart for this data.
→|
Item Head
|
Road
|
Electricity
|
Drinking water
|
Sewerage
|
|
Ammount in crore (Rs.)
|
$43.2$
|
$16.2$
|
$27.00$
|
$21.6$
|
Add the following algebric expressions:
$ \left(4 x y^2-7 x^2 y\right)+\left(12 x^2 y\right)-\left(6 x y^2\right)-\left(3 x^2 y+5 x y^2\right) $
→$ \left(4 x y^2-7 x^2 y\right)+\left(12 x^2 y\right)-\left(6 x y^2\right)-\left(3 x^2 y+5 x y^2\right) $
Verify the following: $(5x + 8)^2- 160x = (5x - 8)^2$
→