Exponents and Powers Class 8 MCQ Maths Chapter 12

MCQ on Exponents and Powers for Class 8

Class 8 Maths Chapter 12 Exponents and Powers MCQ

MCQ of Exponents and Powers Class 8

I. Choose the correct answer.

Question 1.
a^p × a⁵ = a¹², then (a^p)² = __________ .
A) a⁷
B) a⁷²
C) a¹⁴
D) a²⁷
Answer:
C) a¹⁴

Question 2.
3⁰ + 5⁰ (5^-1) = __________ .
A) \(\frac{6}{5}\)
B) 5^-1
C) \(\frac{4}{5}\)
D) \(\frac{5}{5}\)
Answer:
A) \(\frac{6}{5}\)

Question 3.
Multiplicative inverse of 10^-100 = ____________ .
A) \(\frac{1}{10^{100}}\)
B) 1^-100
C) \(\frac{1}{10^{-100}}\)
D) none
Answer:
C) \(\frac{1}{10^{-100}}\)

Question 4.
A^-m = \(\frac{1}{a^m}\), for any __________ .
A) integer (a)
B) any rational (a)
C) non zero integer
D) any of the above
Answer:
C) non zero integer

Question 5.
a × a² × a³ × ………….. × a¹⁰ = _________ .
A) a¹⁰⁰
B) a⁵⁰
C) a²⁵
D) a⁵⁵
Answer:
D) a⁵⁵

Question 6.
p⁵ ÷ p^-7= ____________ .
A) p^-2
B) p²
C) P¹²
D) p^5/-7
Answer:
C) P¹²

Question 7.
(-1)^p = -1, then ‘p’ is ___________ number.
A) odd
B) even
C) prime
D) decimal
Answer:
A) odd

Question 8.
(-4)⁵ ÷ (p)⁸ = (-4)³, then value of p = _________ .
A) -3
B) -4
C) -5
D) -6
Answer:
B) -4

Question 9.
300,000,000 m/sec is in its standard form is ___________ .
A) 3 × 10⁹ m/sec
B) 3 × 10¹⁰ m /sec
C) 3 × 10⁸ m/sec
D) none
Answer:
C) 3 × 10⁸ m/sec

Question 10.
21 × 10^-7 = ___________ .
A) 210000000
B) 2.10000000
C) 0.210000000
D) 0.0000021
Answer:
D) 0.0000021

Question 11.
1.275 × 10^-5 = _________ .
A) 0.00001275
B) 12.75 × 10^-6
C) 0.1275 × 10^-4
D) all the above
Answer:
A) 0.00001275

Question 12.
6.35 × 10²⁶ + 0.635 × 10^-x = 63.5, then x = _________ .
A) -26
B) 27
C) 28
D) 23
Answer:
D) 23

Question 13.
Mass of earth and Moon are 5.97 × 10²⁴ kg and 7.35 × 10²² kg. So, earth Is heavier by _________ kg.
A) 589.65
B) 5.8965 × 10²⁴
C) 58.965 × 10²⁴
D) none
Answer:
B) 5.8965 × 10²⁴

Question 14.
Standard form of 0.000067 = ____________ .
A) 6.7 × 10^-5
B) 67 × 10^-8
C) 0.00067 × 10^-3
D) 670 × 10^-5
Answer:
A) 6.7 × 10^-5

Question 15.
1 micron is 1000000^th part of meter, then expressing in ‘mm’ is _________ (in standard form)
A) 10000^th part of mm
B) 1.0 × 10^-4 mm
C) 1.0 × 10^-6 mm
D) 1.0 × 10^-8 mm
Answer:
B) 1.0 × 10^-4 mm

Question 16.
(\(\frac{a^x}{a^y}\))(\(\frac{a^y}{a^z}\))(\(\frac{a^z}{a^x}\)) = ___________ .
A) a^xyz
B) \(a^{\frac{x+y+z}{x+y+z}}\)
C) \(a^{\frac{x y z}{x y z}}\)
D) 1
Answer:
D) 1

Question 17.
(p^{m + n})^{m – n} . (p^{n + r})^{n – r} . (p^{r + m})^{r – m} = __________ .
A) 1
B) p
C) P^m2n2r2
D) p^{m + n + r}
Answer:
A) 1

Question 18.
(2⁵ ÷ 2⁸)⁵ × 2^-5 = 2^p, then p² = ___________ .
A) 2^-20
B) -20
C) 400
D) -40
Answer:
C) 400

Question 19.
If (-3)^{m – 5} × (-3)^m = (-3)⁹, then (-2)^m = __________ .
A) 7
B) -7
C) -2⁷
D) -2^-7
Answer:
C) -2⁷

Question 20.
(-101)^{2m – 6} × (-101)^{m + 4} = (-101)^-2, then (-101)^2m = __________ .
A) (-101)⁴
B) (-101)²
C) 1
D) none
Answer:
C) 1

For the questions from 21 to 28. Choose the correct answer from options below.
A) Both ‘A’ and ‘R’ are correct and ‘R’ is reason for ‘A’
B) Both ‘A’ and ‘R’ are correct but ‘R’ is not reason for ‘A’.
C) ‘A’ is correct but ‘R’ is false
D) ‘A’ is false but ‘R’ is correct.

Question 21.
Assertion (A) : 2.9 × 10⁸ = 290000000
Reason (R): An exponent refers to the number of times a number is multiplied by itself.
Answer:
A) Both ‘A’ and ‘R’ are correct and ‘R’ is reason for ‘A’

Question 22.
Assertion. (A) : (-1)¹⁰⁰⁵ = 1
Reason (R) : (-1)¹⁰⁰⁰⁷ = -1
Answer:
D) ‘A’ is false but ‘R’ is correct.

Question 23.
Assertion (A) : 2²⁰⁰ × 2²⁰¹ = 2⁴⁰¹
Reason (R) : \(\frac{a^m}{a^n}\) = a^{m – n}
Answer:
B) Both ‘A’ and ‘R’ are correct but ‘R’ is not reason for ‘A’.

Question 24.
Assertion (A) : a⁰ = 1
Reason (R) : \(\frac{a^m}{a^m}\) = a^{m – m} = a⁰ = 1
Answer:
A) Both ‘A’ and ‘R’ are correct and ‘R’ is reason for ‘A’

Question 25.
Assertion (A) : a^m . aⁿ = a^{m + n}
Reason (R): Product of powers property.
Answer:
A) Both ‘A’ and ‘R’ are correct and ‘R’ is reason for ‘A’

Question 26.
Assertion (A) : (a^m)ⁿ = a^mn
Reason (R): Product of powers property.
Answer:
A) Both ‘A’ and ‘R’ are correct and ‘R’ is reason for ‘A’

Question 27.
Assertion (A) : \(\frac{1}{a^n}\) = a^-n
Reason (R) : 1 = a⁰; \(\frac{a^0}{a^n}\) = a^{0 – n} = a^-n
Answer:
D) ‘A’ is false but ‘R’ is correct.

Question 28.
Assertion (A) : 3 × 3 × 3 × 3 = 3⁵
Reason (R) : Exponent refers to the number of times. A number is multiplied by itself.
Answer:
D) ‘A’ is false but ‘R’ is correct.

Question 29.
(-2)³ × (-2)³ ÷ (-2)² = ___________ .
A) -16
B) -8
C) 8
D) 16
Answer:
D) 16

Question 30.
The distance between the Earth and the Moon is approximately 384,000,000 m. Which of these is the correct scientific notation of this distance ?
A) 3.84 × 10⁸ m
B) 3.84 × 10⁶ m
C) 38.4 × 10⁷ m
D) 384 × 10⁶ m
Answer:
A) 3.84 × 10⁸ m

Question 31.
The multiplicative inverse of 3^-5 is
A) 3⁵
B) -3^-5
C) 0
D) 1
Answer:
A) 3⁵

Question 32.
What is the standard form of 0.000216 × 10⁸ ?
A) 2.16 × 10⁴
B) 2.16 × 10⁶
C) 2.16 × 10⁸
D) 2.16 × 10¹²
Answer:
A) 2.16 × 10⁴

Question 33.
Find the value of \(\frac{36^{36}}{18^{18}}\)
A) 36¹⁸
B) 18³⁶
C) 72¹⁸
D) 72³⁶
Answer:
C) 72¹⁸

Question 34.
(\(\frac{1}{2}\))^-5 = __________ .
A) \(\frac{1}{10}\)
B) 10
C) \(\frac{1}{32}\)
D) 32
Answer:
D) 32

Question 35.
If 4^{x + 6} = 8^{x + 2} = 2^y, then find the values of x and y.
A) x = 2 and y = 4
B) x = 2 and y = 16
C) x = 6 and y = 16
D) x = 6 and y = 24
Answer:
D) x = 6 and y = 24

Question 36.
Read the sentences carefully.
Assertion (A) : The value of 2² × 2⁴ is 2⁶.
Reason (R) : a^m × aⁿ = a^{m + n}.
Select the correct option based on the statements given above.
A) A and R are correct and R is the correct explanation of A
B) A and R are correct and R is not the correct explanation of A
C) A is correct, R is wrong .
D) A is wrong, R is correct.
Answer:
A) A and R are correct and R is the correct explanation of A

II. Fill in the blanks.

1. 4¹⁴ = – 2^p ⇒ p = _________ .
Answer:
28

2. 1⁰ + 2⁰ + 3⁰ + (-3)⁰ + (-2)⁰ + (-1)⁰ = _________ .
Answer:
0

3. 1¹⁰⁰ – 100⁰ + (-1)¹⁰¹⁰¹ = _________ .
Answer:
-1

4. Multiplicative inverse of a^m = _________
Answer:
a^-m

5. In 3^a, if the value of exponent decreases by 1, the value becomes _________ of the previous value.
Answer:
\(\frac{1}{3}\)

6. a^-m × a^-n = _________ .
Answer:
a^{– m – n}

7. 2 × 10⁵ + 3 × 10³ + 1 × 10¹ + 2 × 10^-1 = _________ .
Answer:
20301.2

8. Expanded form of 3045.02 = _________ .
Answer:
(3 × 10³) + (4 × 10¹) + (5 × 10⁰) + (2 × 10^-2)

9. (2¹⁰)⁵⁰ = (4P)²⁵ ⇒ p = _________ . .
Answer:
10

10. (2^-1 × 4^-1) + 2^-2 = _________ .
Answer:
\(\frac{1}{2}\)

11. Standard form of 0.00001275 m is ____________ .
Answer:
127.5 × 10⁷m

12. 2^-3 × 8 = ____________ .
Answer:
1

13. 2⁶ × 2⁴ × 2² × 2⁰ = _________ .
Answer:
2¹²

14. Write the standard form of 0.00000564. ___________ .
Answer:
56.4 × 10⁷

III. Match the following.

Question 1.

A	B
1) xy + z = ___________ .	a) 0
2) am – m = ___________ .	b) (\(\frac{x^a}{x^b}\))m
3) (xa – b)m = ___________ .	c) 225
4) (ax)y – axy = ___________ .	d) xy . xz
5) (25)5 = ___________ .	e) 1

Answer:
(1, d) (2, e) (3, b) (4, a) (5, d)

A	B
1) xy + z = ___________ .	d) xy . xz
2) am – m = ___________ .	e) 1
3) (xa – b)m = ___________ .	b) (\(\frac{x^a}{x^b}\))m
4) (ax)y – axy = ___________ .	a) 0
5) (25)5 = ___________ .	d) xy . xz

Question 2.

A	B
1) 0.00006	a) (4 × 102 + 5 × 101 + 6 × 100)
2) 3 × 108 m	b) 6 × 10-5
3) 4-3	c) 300000 km
4) 456	d) a-n
5) \(\frac{1}{a^n}\) =	e) \(\frac{1}{64}\)

Answer:
(1, b) (2, c) (3, e) (4, a) (5, d)

A	B
1) 0.00006	b) 6 × 10-5
2) 3 × 108 m	c) 300000 km
3) 4-3	e) \(\frac{1}{64}\)
4) 456	a) (4 × 102 + 5 × 101 + 6 × 100)
5) \(\frac{1}{a^n}\) =	d) a-n

Class 8 Maths MCQ