Exponents and Powers - Solutions 1
CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 12
Exponents and Powers (Ex. 12.1)
NCERT Solutions
CHAPTER - 12
Exponents and Powers (Ex. 12.1)
1. Evaluate:
(i)
(ii)
(iii) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image003.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image001.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image002.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image003.png)
Ans. (i)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image001.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image004.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image006.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image006.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image007.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image008.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image008.png)
(iii)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image003.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image009.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
=
= 32
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image010.png)
2. Simplify and express the result in power notation with positive exponent:
(i)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image011.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image012.png)
(iii) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image013.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image013.png)
(iv)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image014.png)
(v) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image015.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image015.png)
Ans. (i)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image016.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image017.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image019.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image020.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image021.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image022.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
(iii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image021.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image024.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image021.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image025.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image026.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image027.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image029.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image028.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image029.png)
(iv)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image030.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
=
=
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image034.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image031.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image032.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image033.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image034.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image035.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
(v)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image036.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
=
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image026.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image037.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image038.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image026.png)
3. Find the value of:
(i)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image039.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image040.png)
(iii) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image041.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image041.png)
(iv)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image042.png)
(v) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image043.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image043.png)
Ans.
(i)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image044.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image045.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
=
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image046.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image047.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image029.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image048.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image029.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image049.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
=
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image034.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image050.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image051.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image034.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image052.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image053.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
(iii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image054.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image055.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image056.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
=
= 4 + 9 + 16 = 29
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image057.png)
(iv)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image058.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image059.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image029.png)
(v)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image060.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image061.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image062.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image062.png)
4. Evaluate:
(i)
(ii) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image064.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image063.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image064.png)
Ans. (i)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image065.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image023.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image066.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image067.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image067.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image068.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image069.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image069.png)
5. Find the value of
for which ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image071.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image070.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image071.png)
Ans.
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image072.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image073.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image074.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image073.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image075.png)
Comparing exponents both sides, we get
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image073.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image076.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image073.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image077.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image073.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image078.png)
6. Evaluate:
(i)
(ii) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image080.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image079.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image080.png)
Ans.
(i)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image081.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image082.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image082.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image084.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image083.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image084.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image085.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image086.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image086.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image087.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image088.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image005.png)
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image089.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image089.png)
7. Simplify:
(i)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image090.png)
(ii) ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image091.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image091.png)
Ans. (i)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image092.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image093.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image094.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
=
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image096.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image095.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image096.png)
(ii)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image091.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image097.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image098.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image026.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image034.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image099.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image034.png)
=
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image100.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image018.png)
=
= ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image102.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image101.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image102.png)
= 1
1
3125 ![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image029.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image103.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image103.png)
![](https://media-mycbseguide.s3.amazonaws.com/images/static/ncert/08/maths/12_1/image029.png)
= 3125