Question
Simplify and express the following in exponential form: $\left(3^7 \div 3^5\right)^4$
✓
Answer
We have, $(3^{7} \div 3^{5})^{4}=\Big(\frac{3^{7}}{3^{5}}\Big)^{4}=(3^{7} \div 3^{5})^{4}$
$=(3^{2} \div 3^{4})^{2\times4}$
$\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$
$=3^{8}$
$\Big[\because (\text{a}^{\text{m}})^{\text{n}}={\text{mn}}\Big]$
$=(3^{2} \div 3^{4})^{2\times4}$
$\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$
$=3^{8}$
$\Big[\because (\text{a}^{\text{m}})^{\text{n}}={\text{mn}}\Big]$
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
The area of a rhombus is $=28 \mathrm{~m}^2$. If its perimeter be $28m$, find its altitude.
→A shopkeeper sells mangoes in two types of boxes, one small and one large. A large box contains as many as $8$ small boxes plus $4$ loose mangoes. Set up an equation which gives the number of mangoes in each small box. The number of mangoes in a large box is given to be $100.$
→Can two obtuse angles be complement to each other?
There are four containers that are arranged in the ascending order of their heights. If the height of the smallest container given in the figure is expressed as $\frac{7}{25}\text{x}=10.5\text{cm} $ Find the height of the largest container. 
→Which of the following are pairs of equivalent rational number? $\frac{-13}{7},\frac{39}{-21}$
→Represent the following rational numbers on the number line: $\frac{36}{-5}$
→Simplify and write the following in exponential form:
$\frac{9^8 \times\left(x^2\right)^5}{(27)^4 \times\left(x^3\right)^2}$
→$\frac{9^8 \times\left(x^2\right)^5}{(27)^4 \times\left(x^3\right)^2}$
Find: $\frac{5}{9}$ of 108 metres
→Solve the following equations.
$20 m=100$
→$20 m=100$
Divide:
16.344 by 12
16.344 by 12