Chapter 12 Exponents and Powers mcqs & important questions mathematics | class 8th

MCQ Questions for Class 8 Maths: Ch 12 Exponents and Powers

1. Multiplicative  inverse of 7^-2 is _________ 

(a) 49

(b) 5

(c) 7

(d) -14

► (a) 49

2. (a^m)ⁿ is equal to

(a) a^m+n

(b) a^m-n

(c) a^mn

(d) a^n-m

► (c) a^mn

3. Very small numbers can be expressed in standard form using __________ exponents.

(a) equal

(b) negative

(c) positive

(d) none of these

► (b) negative

4. The Base in the expression 10²⁴ is __________.

(a) 1

(b) 10

(c) 0

(d) 24

► (b) 10

5. Fill in the blank  a^m × aⁿ = a …….. where m and n are natural numbers:-

(a) mn                        

(b) m + n              

(c) m – n

(d) m/n

► (b) m + n

6. The value of 1/3^-2 is equal to

(a) 9

(b) 1

(c) -6

(d) 1/3

► (a) 9

7. When we have to add numbers in standard form, we convert them into numbers with the ________ exponents.
(a) same
(b) different
(c) not equal
(d) None of these
► (a) same

8. The value of 3⁰ is ________.
(a) 0
(b) 3
(c) 1
(d) None of these
► (c) 1

9. Value of (3⁰ + 2⁰) × 5⁰ is
(a) 1
(b) 25
(c) 2
(d) 0
► (c) 2

10. In exponential form 149,600,000,000 m is given by :

(a) 1.496 × 10¹¹ m      

(b) 1.496 × 10⁸ m  

(c) 14.96 × 10⁸ m              

(d) 14.96 × 10¹¹ m

► (a) 1.496 × 10¹¹ m   

11. Evaluate the exponential expression (−n)⁴× (−n)², for n = 5.

(a) 25

(b) 15625

(c) 3125

(d) 625
► (b) 15625

12. Evaluate exponential expression − 2⁵.

(a) 15

(b) -32

(c) 16

(d) none of these
► (b) -32

13. Charge of an electron is 0.000,000,000,000,000,000,16 coulomb and in exponential form it can be written as
(a) 16 × 10^-18 coulomb
(b) 1.6 × 10^-21 coulomb
(c) 1.6 × 10^-19 coulomb           
(d) 16 × 10^-21  coulomb
► (c) 1.6 × 10^-19 coulomb         

14. Find the value of the expression a² for a = 10.

(a) 100

(b) 1

(c) 10

(d) None of these
► (a) 100

15. In 10² the base is

(a) 1

(b) 0

(c) 10

(d) 100
► (c) 10

16. The multiplicative inverse of 2-3 is

(a) 2

(b) 3

(c) 3

(d) 23

► (d) 23

17. 16 is the multiplicative inverse of  

(a) 2^-4

(b) 2⁸

(c) 8²

(d) 2⁴

► (a) 2^-4

18. The standard form of 9030000000 is given by

(a) 9.03 × 10⁹

(b) 90.3 × 10⁷

(c) 903 × 10⁶

(d) 9.03 × 10^-9

► (a) 9.03 × 10⁹

19. The value of 7² is

(a) 7

(b) 49

(c) 2

(d) 14

► (b) 49

20. The value of 1000⁰ is

(a) 0

(b) 1000

(c) 1

(d) None of these

► (c) 1

Exponents and Powers Class 8 Extra Questions Very Short Answer Type

Question 1.
Find the multiplicative inverse of:
(i) 3^-3
(ii) 10^-10
Solution:

Question 2.
Expand the following using exponents.
(i) 0.0523
(ii) 32.005
Solution:

Question 3.
Simplify and write in exponential form.

Solution:

Question 4.
Simplify the following and write in exponential form.

Solution:

Question 5.
Express 8^-4 as a power with the base 2.
Solution:
We have 8 = 2 × 2 × 2 = 2³
8^-4 = (2³)^-4 = 2^3×(-4) = 2^-12

Question 6.
Simplify the following and write in exponential form.
(i) (3⁶ ÷ 3⁸)⁴ × 3^-4
(ii) 127 × 3^-3
Solution:

Question 7.
Find the value of k if (-2)^k+1 × (-2)³ = (-2)⁷
Solution:
(-2)^k+1 × (-2)³ = (-2)⁷
⇒ (-2)^k+1+3 = (-2)⁷
⇒ (-2)^k+4 = (-2)⁷
⇒ k + 4 = 7
⇒ k = 3
Hence, k = 3.

Question 8.
Simplify the following:

Solution:

Question 9.
Find the value of [(−34)−2]2
Solution:

Question 10.
Write the following in standard form
(i) 0 0035
(ii) 365.05
Solution:

Exponents and Powers Class 8 Extra Questions Short Answer Type

Question 11.
Find the value of P if

Solution:

Question 12.

Solution:

Question 13.
Find the value of x if

Solution:

⇒ 3 + x = 18 [Equating the powers of same base]
x = 18 – 3 = 15

Question 14.
Solve the following: (81)^-4 ÷ (729)^2-x = 9^4x
Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.
Find x so that (-5)^x+1 × (-5)⁵ = (-5)⁷ (NCERT Exemplar)
Solution:
(-5)^x+1 × (-5)⁵ = (-5)⁷
(-5)^x+1+5 = (-5)⁷ {a^m × aⁿ = a^m+n}
(-5)^x+6 = (-5)⁷
On both sides, powers have the same base, so their exponents must be equal.
Therefore, x + 6 = 7
x = 7 – 6 = 1
x = 1.