Exponents And Powers(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

EXPONENTS AND POWERS MCQs

Total Questions : 102 | Page 5 of 11 pages

Question 41. A man has many chocolates and he takes

3^{7}

chocolates and distributes it to

3^{4}

students. How many chocolates do each student get if each student should get an equal number of chocolates? [2 MARKS]

Discuss Question

:
Concept: 1 Mark
Answer:1 Mark
Given that,
A man has many chocolates and he takes

3^{7}

chocolates.
He has to distribute them equally between

3^{4}

students.
The number of chocolates a student gets is:

= \frac{3^{7}}{3^{4}}

= 3^{7 - 4}

[

∵ \frac{a^{m}}{a^{n}} = a^{m - n}

]

= 3^{3}

= 27

So, each student will get 27 chocolates.

Question 42. Find the value of 'n' if

{(a^{m})}^{2 n} = a^{2 m}

. Find the numerical value of

a^{2 m}

if a=2 and m=4. [4 MARKS]

Discuss Question

:
Formula: 1 Mark
Value of n: 1 Mark
Numerical value: 1 Mark
Steps: 1 Mark
Given that,

{(a^{m})}^{2 n} = a^{2 m}

a^{2 m n} = a^{2 m}

[∵ {(a^{m})}^{n} = a^{m n}]

Since bases are same, their exponents also should be equal.

\Rightarrow 2 m n = 2 m

\Rightarrow n = \frac{2 m}{2 m}

\Rightarrow n = 1

As per question,
a=2 and m=4
On substituting the values, we get:

a^{2 m}

2^{2 \times 4}

2^{8}

2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2

256

Hence, the required value is 256.

Question 43. Third power of

\frac{1}{4} \times

fourth power of 4 equals to ______.

Discuss Question

Answer: Option C. -> 4
:
C
Third power of

\frac{1}{4} = (\frac{1}{4})^{3}

Fourth power of 4 is equal to

4^{4}

(\frac{1}{4})^{3} \times 4^{4}

\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times 4 \times 4 \times 4 \times 4

\frac{4 \times 4 \times 4 \times 4}{4 \times 4 \times 4}

\frac{4^{4}}{4^{3}}

= 4

Question 44. Express 5126000 in standard form.

0.5126×107
5.126×106
51.26×105
5126×103

Discuss Question

Answer: Option B. -> 5.126×106
:
B
In standard form, any number is expressed in powers of 10. The decimal number must be in between 1 and 10.

5.126 \times 1000000 = 5.126 \times 10^{6}

Question 45.

2^{3} \times 3^{3}

___

Discuss Question

2^{3} \times 3^{3} = (2 \times 3)^{3} = 6^{3} = 216

Question 46. The value of

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

Discuss Question

:
Notice that here the two terms

4^{3}

and

2^{3}

have different bases, but the same exponents.

4^{3} \times 2^{3} = (4 \times 4 \times 4) \times (2 \times 2 \times 2)

= (4 \times 2) \times (4 \times 2) \times (4 \times 2) = 8^{3} = 512

Question 47. If a = 2 and b = 3, find the value of

(a^{b})^{a}

Discuss Question

Answer: Option C. -> 64
:
C
On substitutinga = 2 and b = 3, we get

(2^{3})^{2} = 2^{3 \times 2} [∵ (x^{m})^{n} = x^{(m \times n)}]

= 2^{6}

= 64

Question 48. Express

256 \times 243

in exponential form.

28×35
27×34
26×33
22×32

Discuss Question

Answer: Option A. -> 28×35
:
A
We can write:

256 = (2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2) = 2^{8}

243 = (3 \times 3 \times 3 \times 3 \times 3) = 3^{5}

∴ 256 \times 243 = 2^{8} \times 3^{5}

Question 49.

3 \times 1000 + 2 \times 10 + \frac{4}{10} + \frac{3}{1000}

is the expanded form of the number ____.

3200.430
3002.403
32.430
3020.403

Discuss Question

Answer: Option D. -> 3020.403
:
D

3 \times 1000 + 2 \times 10 + \frac{4}{10} + \frac{3}{1000}

= 3000 + 20 + 0.4 + 0.003

= 3020.403

Question 50.

Express 343 as a power of 7.

$7^{2}$
$7^{3}$
$7^{4}$
$7^{0}$

Discuss Question

Answer: Option B. ->

7^{3}

:
B

343 can be written as
$343 = 7 \times 7 \times 7$
so, $343 = 7^{3}$

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