Question
Find following product:
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
✓
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:
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}×\text{x}^2)×(\text{y}×\text{y})×\text{z}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}^{1+2}\big)×\big(\text{y}^{1+1}\big)×\text{z}^2$
$=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
Thus, the answer is $=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
We have:
$\frac{1}{4}\text{xy}×\frac{2}{3}\text{x}^2\text{yz}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}×\text{x}^2)×(\text{y}×\text{y})×\text{z}^2$
$=\big(\frac{1}{4}×\frac{2}{3}\big)×\big(\text{x}^{1+2}\big)×\big(\text{y}^{1+1}\big)×\text{z}^2$
$=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
Thus, the answer is $=\frac{1}{6}\text{x}^3\text{y}^2\text{z}^2$
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
Three numbers are in the ratio $1 : 2 : 3.$ The sum of their cubes is $98784$. Find the numbers.
→Is it possible to construct a quadrilateral $ROAM$ in which $RO = 4cm, OA = 5cm, \angle\text{O}=120^\circ,\angle\text{R}=105^\circ\ \text{and}\ \angle\text{A}=135^\circ$? If not, why?
→$A$ and $B$, working together can finish a piece of work in $6$ days, while $A$ alone can do it in $9$ days. How much time will $B$ alone take to finish it?
→Find the greatest number of five digits which is a perfect square. Also find the square root of the number so obtained.
A carpenter charged Rs. $2500$ for making a bed. The cost of materials used is Rs. $1100$ and the labour charges are Rs. $200/hr.$ For how many hours did the carpenter work?
→A group of $360$ people were asked to vote for their favourite season from the three seasons rainy, winter and summer.
Find the central angle of each sector?
→| Season | No. of votes |
|---|---|
Summer  |
$90$ |
Rainy  |
$120$ |
Winter  |
$150$ |
List price of a washing machine is $Rs. 9,000$. If the dealer allows a discount of $5\%$ on the cash payment, how much will a customer pay to the dealer in cash, if the rate of $VAT$ is $10\%.$
→If $\Big(\text{x}-\frac{1}{\text{x}}\Big)=4$ find the value of: $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)$
→Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.
The population of a place increased to $54,000$ in $2003$ at a rate of $5\%$ per annum
$(i)$ find the population in $2001$.
$(ii)$ what would be its population in $2005$?
→$(i)$ find the population in $2001$.
$(ii)$ what would be its population in $2005$?