Question
Find following product: $\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$
✓
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:
$\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]×\big(\text{a}^2×\text{a}^3\big)×\big(\text{b}^2×\text{b}^2\big)×\text{c}^2$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]\times\big(\text{a}^{2+3}\big)\times\big(\text{b}^{2+2}\big)\times\text{c}^2$
Thus, the answer is $−\frac{1}{6}\text{a}^5\text{b}^4\text{c}^2.$
We have:
$\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]×\big(\text{a}^2×\text{a}^3\big)×\big(\text{b}^2×\text{b}^2\big)×\text{c}^2$
$=\big[\big(-\frac{1}{27}×\frac{9}{2}\big)\big]\times\big(\text{a}^{2+3}\big)\times\big(\text{b}^{2+2}\big)\times\text{c}^2$
Thus, the answer is $−\frac{1}{6}\text{a}^5\text{b}^4\text{c}^2.$
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
By using the formula, find the amount and compound interest on.
$Rs. 31250$ for $3$ years at $8\%$ per annum compounded annually.
→$Rs. 31250$ for $3$ years at $8\%$ per annum compounded annually.
How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of $10\%$ on the marked price, he gains $8\%?$
→$10$ people can dig a trench in $6$ days. How many people can dig it in $4$ days?
→In a right angled $\triangle \text{ABC}, \angle \text{B}=90^{\circ}$.
(i) If $\text{AB}=6 \text{ cm}$ and $\text{BC}=8 \text{ cm}$, find $\text{AC}$.
(ii) If $\text{AC}=13 \text{ cm}$ and $\text{BC}=5 \text{ cm}$, find $\text{AB}$.
→(i) If $\text{AB}=6 \text{ cm}$ and $\text{BC}=8 \text{ cm}$, find $\text{AC}$.
(ii) If $\text{AC}=13 \text{ cm}$ and $\text{BC}=5 \text{ cm}$, find $\text{AB}$.
Bansi has $3$ times as many two$-$rupee coins as he has five-rupee coins. If he has in all a sum of $₹ 77$, how many coins of each denomination does he have?
→Find the amount of Rs. $2400$ after $3$ years, when the interest is compounded annually at the rate of $20\%$ per annum.
→Find the volume of each of the given figure if volume $=$ base area $\times $ height.
→Find the surface area of a cuboid whose:
Length $= 6\ dm,$ breadth $= 8\ dm,$ height $= 10\ dm.$
→Length $= 6\ dm,$ breadth $= 8\ dm,$ height $= 10\ dm.$
In a quadrilateral $PQRS, \angle\text{P}=50^\circ,\angle\text{Q}=50^\circ,\angle\text{R}=50^\circ,\text{Find}\angle\text{S}$. Is this quadrilateral convex or concave?
→Find the smallest number by which the given number must bew multiplied so that the product is a perfect square: $12150$
→