Exponents And Powers(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

EXPONENTS AND POWERS MCQs

Total Questions : 58 | Page 1 of 6 pages

Question 1. The exponent of c after simplifying

(3 a b)^{2}

(- 5 a^{2} b c^{4})^{2}

is
___

Discuss Question

(3 a b)^{2}

(- 5 a^{2} b c^{4})^{2}

= (9

a^{2}

b^{2}

) × (25

a^{4}

b^{2}

c^{8}

)
= 225

a^{6}

b^{4}

c^{8}

Exponent of c = 8

Question 2. Simplify

{(2^{5} \div 2^{8})}^{5}

2^{- 5} .

1210
1220
12(−15)
12(−5)

Discuss Question

Answer: Option B. -> 1220
:
B

{(2^{5} \div 2^{8})}^{5} \times 2^{- 5} = {(\frac{2^{5}}{2^{8}})}^{5} \times 2^{- 5}

= {(2^{5 - 8})}^{5} \times 2^{- 5} (∵ \frac{a^{m}}{a^{n}} = a^{m - n})

= {(2^{- 3})}^{5} \times 2^{- 5}

= 2^{- 15} \times 2^{- 5} (∵ (a^{m})^{n} = a^{m n})

= 2^{- 15 - 5} (∵ a^{m} \times a^{n} = a^{m + n})

= 2^{- 20}

= \frac{1}{2^{20}} (∵ a^{- m} = \frac{1}{a^{m}})

Question 3. Find the value of ‘m‘ if

(- 2)^{2} \times (- 5)^{3} = 50 m

Discuss Question

Answer: Option A. -> -10
:
A

(- 2)^{2} \times (- 5)^{3} = 50 m

\Rightarrow 4 \times (- 125) = 50 m

\Rightarrow - 500 = 50 m

\Rightarrow m = - 10

Question 4. In standard form 21600000 is written as___________.

2.16×107
216×107
2.16×105
216×1000000

Discuss Question

Answer: Option A. -> 2.16×107
:
A
21600000= 2.16 x 10000000
Therefore, in standard form 21600000 is written as :

2.16 \times 10^{7}

Question 5.

(9 \times 10^{- 2}) + (9 \times 10^{3})

in usual form is given by

9000.09
900.9
9000.9
900.09

Discuss Question

Answer: Option A. -> 9000.09
:
A
The usual forms of the expressions

9 \times 10^{- 2}

and

9 \times 10^{3}

are given by0.09 and 9000.
Thus, 9000 + 0.09 = 9000.09.

Question 6. Express

4.95 \times 10^{5}

in usual form.

49500
4950
495000
4950000

Discuss Question

Answer: Option C. -> 495000
:
C

4.95 \times 10^{5} = 4.95 \times 100000 = 495000

Question 7. Simplify and write in exponential form:

4^{3} \times 4^{- 2} \times 16^{2}

Discuss Question

Answer: Option C. -> 45
:
C
Given expression is

4^{3} \times 4^{- 2} \times 16^{2} = 4^{3} \times 4^{- 2} \times {((4)^{2})}^{2} = 4^{3} \times 4^{- 2} \times 4^{4} (∵ (a^{m})^{n} = a^{m n}) = 4^{3 - 2 + 4} (∵ a^{m} \times a^{n} = a^{m + n}) = 4^{5}

Question 8. Find the multiplicative inverse of

10^{- 7}

10−2
102
107
106

Discuss Question

Answer: Option C. -> 107
:
C
Multiplicative inverse of a non-zero

x

\frac{1}{x}

; so that when these two are multiplied, the product value is 1. Therefore, the multiplicative inverse of

10^{- 7}

should be a number which when multiplied with

10^{- 7}

gives 1.
Let the multiplicative inverse of

10^{- 7}

x .

Then,

10^{- 7} \times x = 1.

\Rightarrow x = \frac{1}{10^{- 7}} = 10^{7}

(∵ a^{- n} = \frac{1}{a^{n}} ⟹ \frac{1}{a^{- n}} = \frac{1}{\frac{1}{a^{n}}} = a^{n})

Thus, the multiplicative inverse of

10^{- 7}

10^{7} .

Question 9. Find the value of

7^{- 3}

343
1343
121
149

Discuss Question

Answer: Option B. -> 1343
:
B
We know that

a^{- m} = \frac{1}{a^{m}}

for any non-zero integer

a

and integer

m .

⟹ 7^{- 3} = \frac{1}{7^{3}}

= \frac{1}{7 \times 7 \times 7} = \frac{1}{343}

Question 10. If 3676.48 can be written in expanded form as:

3 \times 10^{a} + b \times 10^{2} + 7 \times 10^{c} + 6 \times 10^{0} + 4 \times 10^{d} + e \times 10^{- 2}

Find the value of a + b - c - d - e .

Discuss Question

:
3676.48 can be written in expanded form as:

3 \times 10^{3} + 6 \times 10^{2} + 7 \times 10^{1} + 6 \times 10^{0} + 4 \times 10^{- 1} + 8 \times 10^{- 2}

a = 3, b = 6, c = 1, d = - 1, e = 8 a + b - c - d - e = 3 + 6 - 1 + 1 - 8 = 1

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