Exponents and Powers Class 7 Extra Questions Maths Chapter 13
Extra Questions for Class 7 Maths Chapter 13 Exponents and Powers
Exponents and Powers Class 7 Extra Questions Very Short Answer Type
Question 1.
Express 343 as a power of 7.
Solution:
We have 343 = 7 × 7 × 7 = 7
3
Thus, 343 = 7
3
Question 2.
Which is greater 3
2
or 2
3
?
Solution:
We have 3
2
= 3 × 3 = 9
2
3
= 2 × 2 × 2 = 8
Since 9 > 8
Thus, 3
2
> 2
3
Question 3.
Express the following number as a powers of prime factors:
(i) 144
(ii) 225
Solution:
(i) We have
144 = 2 × 2 × 2 × 2 × 3 × 3 = 2
4
× 3
2
Thus, 144 = 2
4
× 3
2
(ii) We have
225 = 3 × 3 × 5 × 5 = 3
2
× 5
2
Thus, 225 = 3
2
× 5
2
Question 4.
Find the value of:
(i) (-1)
1000
(ii) (1)
250
(iii) (-1)
121
(iv) (10000)
0
Solution:
(i) (-1)
1000
= 1 [∵ (-1)
even number
= 1]
(ii) (1)
250
= 1 [∵ (1)
even number
= 1]
(iii) (-1)
121
= -1 [∵ (-1)
odd number
= -1]
(iv) (10000)
0
= 1 [∵ a
0
= 1]
Question 5.
Express the following in exponential form:
(i) 5 × 5 × 5 × 5 × 5
(ii) 4 × 4 × 4 × 5 × 5 × 5
(iii) (-1) × (-1) × (-1) × (-1) × (-1)
(iv) a × a × a × b × c × c × c × d × d
Solution:
(i) 5 × 5 × 5 × 5 × 5 = (5)
5
(ii) 4 × 4 × 4 × 5 × 5 × 5 = 4
3
× 5
3
(iii) (-1) × (-1) × (-1) × (-1) × (-1) = (-1)
5
(iv) a × a × a × b × c × c × c × d × d = a
3
b
1
c
3
d
2
Question 6.
Express each of the following as product of powers of their prime factors:
(i) 405
(ii) 504
(iii) 500
Solution:
(i) We have
405 = 3 × 3 × 3 × 3 × 5 = 3
4
× 5
1
Thus, 405 = 3
4
× 5
1
(ii) We have
504 = 2 × 2 × 2 × 3 × 3 × 7 = 2
3
× 3
2
× 7
1
Thus, 504 = 2
3
× 3
2
× 7
1
(iii) We have
500 = 2 × 2 × 5 × 5 × 5 = 2
2
× 5
3
Thus, 500 = 2
2
× 5
3
Question 7.
Simplify the following and write in exponential form:
(i) (5
2
)
3
(ii) (2
3
)
3
(iii) (a
b
)
c
(iv) [(5)
2
]
2
Solution:
(i) (5
2
)
3
= 5
2×3
= 5
6
(ii) (2
3
)
3
= 2
3×3
= 2
9
(iii) (a
b
)
c
= a
b×c
= a
bc
(iv) [(5)
2
]
2
= 5
2×2
= 5
4
Question 8.
Verify the following:
Solution:
Question 9.
Simplify:
Solution:
Question 10.
Simplify and write in exponential form:
Solution:
Exponents and Powers Class 7 Extra Questions Short Answer Type
Question 11.
Express each of the following as a product of prime factors is the exponential form:
(i) 729 × 125
(ii) 384 × 147
Solution:
(i) 729 × 125 = 3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5 = 3
6
× 5
3
Thus, 729 × 125 = 3
6
× 5
3
(ii) 384 × 147 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7 = 2
7
× 3
2
× 7
2
Thus, 384 × 147 = 2
7
× 3
2
× 7
2
Question 12.
Simplify the following:
(i) 10
3
× 9
0
+ 3
3
× 2 + 7
0
(ii) 6
3
× 7
0
+ (-3)
4
– 9
0
Solution:
(i) 10
3
× 9
0
+ 3
3
× 2 + 7
0
= 1000 + 54 + 1
= 1055
(ii) 6
3
× 7
0
+ (-3)
4
– 9
0
= 216 × 1 + 81 – 1
= 216 + 80
= 296
Question 13.
Write the following in expanded form:
(i) 70,824
(ii) 1,69,835
Solution:
(i) 70,824
= 7 × 10000 + 0 × 1000 + 8 × 100 + 2 × 10 + 4 × 10
0
= 7 × 10
4
+ 8 × 10
2
+ 2 × 10
1
+ 4 × 10
0
(ii) 1,69,835
= 1 × 100000 + 6 × 10000 + 9 × 1000 + 8 × 100 + 3 × 10 + 5 × 10
0
= 1 × 10
5
+ 6 × 10
4
+ 9 × 10
3
+ 8 × 10
2
+ 3 × 10
1
+ 5 × 10
0
Question 14.
Find the number from each of the expanded form:
(i) 7 × 10
8
+ 3 × 10
5
+ 7 × 10
2
+ 6 × 10
1
+ 9
(ii) 4 × 10
7
+ 6 × 10
3
+ 5
Solution:
(i) 7 × 10
8
+ 3 × 10
5
+ 7 × 10
2
+ 6 × 10
1
+ 9
= 7 × 100000000 + 3 × 100000 + 7 × 100 + 6 × 10 + 9
= 700000000 + 300000 + 700 + 60 + 9
= 700300769
(ii) 4 × 10
7
+ 6 × 10
3
+ 5
= 4 × 10000000 + 6 × 1000 + 5
= 40000000 + 6000 + 5
= 40006005
Question 15.
Find the value of k in each of the following:
Solution:
Question 16.
Find the value of
(a) 3
0
÷ 4
0
(b) (8
0
– 2
0
) ÷ (8
0
+ 2
0
)
(c) (2
0
+ 3
0
+ 4
0
) – (4
0
– 3
0
– 2
0
)
Solution:
(a) We have 3
0
÷ 4
0
= 1 ÷ 1 = 1 [∵ a
0
= 1]
(6) (8
0
– 2
0
) ÷ (8
0
+ 2
0
) = (1 – 1) ÷ (1 + 1) = 0 ÷ 2 = 0
(c) (2
0
+ 3
0
+ 4
0
) – (4
0
– 3
0
– 2
0
)
= (1 + 1 + 1) – (1 – 1 – 1) [∵ a
0
= 1]
= 3 – 1
= 2
Question 17.
Express the following in standard form:
(i) 8,19,00,000
(ii) 5,94,00,00,00,000
(iii) 6892.25
Solution:
(i) 8,19,00,000 = 8.19 × 10
7
(ii) 5,94,00,00,00,000 = 5.94 × 10
11
(iii) 6892.25 = 6.89225 × 10
3
Question 18.
Evaluate:
Solution:
Exponents and Powers Class 7 Extra Questions Higher Order Thinking Skills (HOTS) Type
Question 19.
Find the value of x, if
Solution:
Question 20.
Solution:
