Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > NCERT Exemplar Solutions: Exponents & Powers
NCERT Exemplar Solutions: Exponents & Powers | Mathematics (Maths) Class 7 PDF Download
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Page 1
Exercise
In questions 1 to 22, there are four options, out of which one is
correct. Write the correct one.
1. [(–3)
2
]
3
is equal to
(a) (–3)
8
(b) (–3)
6
(c) (–3)
5
(d) (–3)
23
Solution:
We know that, (a
m
)
n
= (a)
m×n
. Therefore,
[(-3)
2
]
3
= [(-3)]
2×3
= (-3)
6
So, option (b) is correct.
2. For a non-zero rational number x, x
8
÷ x
2
is equal to
(a) x
4
(b) x
6
(c) x
10
(d) x
16
Solution:
We know that, when base is same, the powers get subtracted in division. Therefore,
6
2 8
2
8
2 8
x ÷ x
x
x
x
x
=
=
=
-
So, option (b) is correct.
3. x is a non-zero rational number. Product of the square of x with the cube
of x is equal to the
(a) second power of x (b) third power of x (c) fifth power of x (d)
sixth power of x
Solution:
Square of x is x
2
And cube of x is x
3
Now, product will be x
2
× x
3
= x
5
i.e., fifth power of x.
So, option (c) is correct.
4. For any two non-zero rational numbers x and y, x
5
÷ y
5
is equal to
(a) (x÷y)
1
(b) (x÷y)
0
(c) (x÷y)
5
(d) (x÷y)
10
Solution:
We know that, a
m
÷ b
m
= (a ÷ b)
m
Chapter - 11
Exponent
Page 2
Exercise
In questions 1 to 22, there are four options, out of which one is
correct. Write the correct one.
1. [(–3)
2
]
3
is equal to
(a) (–3)
8
(b) (–3)
6
(c) (–3)
5
(d) (–3)
23
Solution:
We know that, (a
m
)
n
= (a)
m×n
. Therefore,
[(-3)
2
]
3
= [(-3)]
2×3
= (-3)
6
So, option (b) is correct.
2. For a non-zero rational number x, x
8
÷ x
2
is equal to
(a) x
4
(b) x
6
(c) x
10
(d) x
16
Solution:
We know that, when base is same, the powers get subtracted in division. Therefore,
6
2 8
2
8
2 8
x ÷ x
x
x
x
x
=
=
=
-
So, option (b) is correct.
3. x is a non-zero rational number. Product of the square of x with the cube
of x is equal to the
(a) second power of x (b) third power of x (c) fifth power of x (d)
sixth power of x
Solution:
Square of x is x
2
And cube of x is x
3
Now, product will be x
2
× x
3
= x
5
i.e., fifth power of x.
So, option (c) is correct.
4. For any two non-zero rational numbers x and y, x
5
÷ y
5
is equal to
(a) (x÷y)
1
(b) (x÷y)
0
(c) (x÷y)
5
(d) (x÷y)
10
Solution:
We know that, a
m
÷ b
m
= (a ÷ b)
m
Chapter - 11
Exponent
x
5
÷ y
5
= (x ÷ y)
5
So, option (c) is correct.
5. a
m
× a
n
is equal to
(a) (a
2
)
mn
(b) a
m–n
(c) a
m+n
(d) a
mn
Solution:
We know that when base is same, power gets added in multiplication. Therefore,
a
m
× a
n
= (a)
m + n
So, option (c) is correct.
6. (1
0
+ 2
0
+ 3
0
) is equal to
(a) 0 (b) 1 (c) 3 (d) 6
Solution:
We know that any number raised to the power zero is equal to 1. Therefore,
(1
0
+ 2
0
+ 3
0
) = (1 + 1 + 1)
= 3
So, option (c) is correct.
7. Value of (10
22
+ 10
20
)/10
20
is
(a) 10 (b) 10
42
(c) 101 (d) 10
22
Solution:
( ) ( )
101
1 100
10
1 10 10
10
10 10
20
2 20
20
20 22
=
+ =
+
=
+
So, option (c) is correct.
8. The standard form of the number 12345 is
(a) 1234.5 × 10
1
(b) 123.45 × 10
2
(c) 12.345 × 10
3
(d) 1.2345 × 10
4
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 12345 = 1.2345 × 10
4
.
So, option (d) is correct.
9. If 2
1998
– 2
1997
– 2
1996
+ 2
1995
= K.2
1995
, then the value of K is
(a) 1 (b) 2 (c) 3 (d) 4
Page 3
Exercise
In questions 1 to 22, there are four options, out of which one is
correct. Write the correct one.
1. [(–3)
2
]
3
is equal to
(a) (–3)
8
(b) (–3)
6
(c) (–3)
5
(d) (–3)
23
Solution:
We know that, (a
m
)
n
= (a)
m×n
. Therefore,
[(-3)
2
]
3
= [(-3)]
2×3
= (-3)
6
So, option (b) is correct.
2. For a non-zero rational number x, x
8
÷ x
2
is equal to
(a) x
4
(b) x
6
(c) x
10
(d) x
16
Solution:
We know that, when base is same, the powers get subtracted in division. Therefore,
6
2 8
2
8
2 8
x ÷ x
x
x
x
x
=
=
=
-
So, option (b) is correct.
3. x is a non-zero rational number. Product of the square of x with the cube
of x is equal to the
(a) second power of x (b) third power of x (c) fifth power of x (d)
sixth power of x
Solution:
Square of x is x
2
And cube of x is x
3
Now, product will be x
2
× x
3
= x
5
i.e., fifth power of x.
So, option (c) is correct.
4. For any two non-zero rational numbers x and y, x
5
÷ y
5
is equal to
(a) (x÷y)
1
(b) (x÷y)
0
(c) (x÷y)
5
(d) (x÷y)
10
Solution:
We know that, a
m
÷ b
m
= (a ÷ b)
m
Chapter - 11
Exponent
x
5
÷ y
5
= (x ÷ y)
5
So, option (c) is correct.
5. a
m
× a
n
is equal to
(a) (a
2
)
mn
(b) a
m–n
(c) a
m+n
(d) a
mn
Solution:
We know that when base is same, power gets added in multiplication. Therefore,
a
m
× a
n
= (a)
m + n
So, option (c) is correct.
6. (1
0
+ 2
0
+ 3
0
) is equal to
(a) 0 (b) 1 (c) 3 (d) 6
Solution:
We know that any number raised to the power zero is equal to 1. Therefore,
(1
0
+ 2
0
+ 3
0
) = (1 + 1 + 1)
= 3
So, option (c) is correct.
7. Value of (10
22
+ 10
20
)/10
20
is
(a) 10 (b) 10
42
(c) 101 (d) 10
22
Solution:
( ) ( )
101
1 100
10
1 10 10
10
10 10
20
2 20
20
20 22
=
+ =
+
=
+
So, option (c) is correct.
8. The standard form of the number 12345 is
(a) 1234.5 × 10
1
(b) 123.45 × 10
2
(c) 12.345 × 10
3
(d) 1.2345 × 10
4
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 12345 = 1.2345 × 10
4
.
So, option (d) is correct.
9. If 2
1998
– 2
1997
– 2
1996
+ 2
1995
= K.2
1995
, then the value of K is
(a) 1 (b) 2 (c) 3 (d) 4
Solution:
( )
( )
3 2
1 2 4 8 2
1 2 2 2 2 2 2 2 2
1995
1995
1 2 3 1995 1995 1996 1997 1998
? =
+ - - =
+ - - = + - -
This implies, K = 3
So, option (c) is correct.
10. Which of the following is equal to 1?
(a) 2
0
+ 3
0
+ 4
0
(b) 2
0
× 3
0
× 4
0
(c) (3
0
– 2
0
) × 4
0
(d) (3
0
– 2
0
) × (3
0
+2
0
)
Solution:
2
0
× 3
0
× 4
0
= 1 × 1 × 1
= 1
So, option (b) is correct.
11. In standard form, the number 72105.4 is written as 7.21054 × 10
n
where
n is equal to
(a) 2 (b) 3 (c) 4 (d) 5
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 72105.4 = 7.21054 × 10
4
.
So, option (c) is correct.
12. Square of (-2/3) is
(a) -2/3 (b) 2/3 (c) -4/9 (d) 4/9
Solution:
9
4
3
2
3
2
3
2
2
=
?
?
?
?
?
?
- ? ?
?
?
?
?
?
- = ?
?
?
?
?
?
-
So, option (d) is correct.
13. Cube of (-1/4) is
(a) –1/12 (b) 1/16 (c) -1/64 (d) 1/64
Solution:
Page 4
Exercise
In questions 1 to 22, there are four options, out of which one is
correct. Write the correct one.
1. [(–3)
2
]
3
is equal to
(a) (–3)
8
(b) (–3)
6
(c) (–3)
5
(d) (–3)
23
Solution:
We know that, (a
m
)
n
= (a)
m×n
. Therefore,
[(-3)
2
]
3
= [(-3)]
2×3
= (-3)
6
So, option (b) is correct.
2. For a non-zero rational number x, x
8
÷ x
2
is equal to
(a) x
4
(b) x
6
(c) x
10
(d) x
16
Solution:
We know that, when base is same, the powers get subtracted in division. Therefore,
6
2 8
2
8
2 8
x ÷ x
x
x
x
x
=
=
=
-
So, option (b) is correct.
3. x is a non-zero rational number. Product of the square of x with the cube
of x is equal to the
(a) second power of x (b) third power of x (c) fifth power of x (d)
sixth power of x
Solution:
Square of x is x
2
And cube of x is x
3
Now, product will be x
2
× x
3
= x
5
i.e., fifth power of x.
So, option (c) is correct.
4. For any two non-zero rational numbers x and y, x
5
÷ y
5
is equal to
(a) (x÷y)
1
(b) (x÷y)
0
(c) (x÷y)
5
(d) (x÷y)
10
Solution:
We know that, a
m
÷ b
m
= (a ÷ b)
m
Chapter - 11
Exponent
x
5
÷ y
5
= (x ÷ y)
5
So, option (c) is correct.
5. a
m
× a
n
is equal to
(a) (a
2
)
mn
(b) a
m–n
(c) a
m+n
(d) a
mn
Solution:
We know that when base is same, power gets added in multiplication. Therefore,
a
m
× a
n
= (a)
m + n
So, option (c) is correct.
6. (1
0
+ 2
0
+ 3
0
) is equal to
(a) 0 (b) 1 (c) 3 (d) 6
Solution:
We know that any number raised to the power zero is equal to 1. Therefore,
(1
0
+ 2
0
+ 3
0
) = (1 + 1 + 1)
= 3
So, option (c) is correct.
7. Value of (10
22
+ 10
20
)/10
20
is
(a) 10 (b) 10
42
(c) 101 (d) 10
22
Solution:
( ) ( )
101
1 100
10
1 10 10
10
10 10
20
2 20
20
20 22
=
+ =
+
=
+
So, option (c) is correct.
8. The standard form of the number 12345 is
(a) 1234.5 × 10
1
(b) 123.45 × 10
2
(c) 12.345 × 10
3
(d) 1.2345 × 10
4
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 12345 = 1.2345 × 10
4
.
So, option (d) is correct.
9. If 2
1998
– 2
1997
– 2
1996
+ 2
1995
= K.2
1995
, then the value of K is
(a) 1 (b) 2 (c) 3 (d) 4
Solution:
( )
( )
3 2
1 2 4 8 2
1 2 2 2 2 2 2 2 2
1995
1995
1 2 3 1995 1995 1996 1997 1998
? =
+ - - =
+ - - = + - -
This implies, K = 3
So, option (c) is correct.
10. Which of the following is equal to 1?
(a) 2
0
+ 3
0
+ 4
0
(b) 2
0
× 3
0
× 4
0
(c) (3
0
– 2
0
) × 4
0
(d) (3
0
– 2
0
) × (3
0
+2
0
)
Solution:
2
0
× 3
0
× 4
0
= 1 × 1 × 1
= 1
So, option (b) is correct.
11. In standard form, the number 72105.4 is written as 7.21054 × 10
n
where
n is equal to
(a) 2 (b) 3 (c) 4 (d) 5
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 72105.4 = 7.21054 × 10
4
.
So, option (c) is correct.
12. Square of (-2/3) is
(a) -2/3 (b) 2/3 (c) -4/9 (d) 4/9
Solution:
9
4
3
2
3
2
3
2
2
=
?
?
?
?
?
?
- ? ?
?
?
?
?
?
- = ?
?
?
?
?
?
-
So, option (d) is correct.
13. Cube of (-1/4) is
(a) –1/12 (b) 1/16 (c) -1/64 (d) 1/64
Solution:
64
1
4
1
4
1
4
1
4
1
3
- =
?
?
?
?
?
?
- ? ?
?
?
?
?
?
- ? ?
?
?
?
?
?
- = ?
?
?
?
?
?
-
So, option (c) is correct.
14. Which of the following is not equal to (–5/4)
4
?
(a) (– 5)
4
/(4
4
) (b) (5
4
)/(– 4 )
4
(c) -(5
4
/ 4
4
) (d) (-5/4) x (-5/4) x (-5/4) x
(-5/4)
Solution:
4
5 5 5 5 5
4 4 4 4 4
625
256
? ? ? ? ? ? ? ? ? ?
- = - ? - ? - ? -
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
=
44
44
55
44
625
256
??
- = -
??
??
=-
So, option (c) is correct.
15. Which of the following is not equal to 1 ?
(a) (2
3
× 3
2
)/4 × 18 (b) [(-2)
3
× (-2)
4
] ÷ (-2)
7
(c) (3
0
× 5
3
)/(5×25) (d) 2
4
/(7
0
+ 3
0
)
3
Solution:
( )
( )
44
33
00
4
3
22
11
73
2
2
2
=
+
+
=
=
So, option (d) is correct.
16. (2/3)
3
× (5/7)
3
is equal to
(a) (2/3 × 5/7)
9
(b) (2/3 × 5/7)
6
(c) (2/3 × 5/7)
3
(d) (2/3 × 5/7)
0
Solution:
We know that, when power is same bases get multiplied in case of multiplication of
exponents, therefore,
Page 5
Exercise
In questions 1 to 22, there are four options, out of which one is
correct. Write the correct one.
1. [(–3)
2
]
3
is equal to
(a) (–3)
8
(b) (–3)
6
(c) (–3)
5
(d) (–3)
23
Solution:
We know that, (a
m
)
n
= (a)
m×n
. Therefore,
[(-3)
2
]
3
= [(-3)]
2×3
= (-3)
6
So, option (b) is correct.
2. For a non-zero rational number x, x
8
÷ x
2
is equal to
(a) x
4
(b) x
6
(c) x
10
(d) x
16
Solution:
We know that, when base is same, the powers get subtracted in division. Therefore,
6
2 8
2
8
2 8
x ÷ x
x
x
x
x
=
=
=
-
So, option (b) is correct.
3. x is a non-zero rational number. Product of the square of x with the cube
of x is equal to the
(a) second power of x (b) third power of x (c) fifth power of x (d)
sixth power of x
Solution:
Square of x is x
2
And cube of x is x
3
Now, product will be x
2
× x
3
= x
5
i.e., fifth power of x.
So, option (c) is correct.
4. For any two non-zero rational numbers x and y, x
5
÷ y
5
is equal to
(a) (x÷y)
1
(b) (x÷y)
0
(c) (x÷y)
5
(d) (x÷y)
10
Solution:
We know that, a
m
÷ b
m
= (a ÷ b)
m
Chapter - 11
Exponent
x
5
÷ y
5
= (x ÷ y)
5
So, option (c) is correct.
5. a
m
× a
n
is equal to
(a) (a
2
)
mn
(b) a
m–n
(c) a
m+n
(d) a
mn
Solution:
We know that when base is same, power gets added in multiplication. Therefore,
a
m
× a
n
= (a)
m + n
So, option (c) is correct.
6. (1
0
+ 2
0
+ 3
0
) is equal to
(a) 0 (b) 1 (c) 3 (d) 6
Solution:
We know that any number raised to the power zero is equal to 1. Therefore,
(1
0
+ 2
0
+ 3
0
) = (1 + 1 + 1)
= 3
So, option (c) is correct.
7. Value of (10
22
+ 10
20
)/10
20
is
(a) 10 (b) 10
42
(c) 101 (d) 10
22
Solution:
( ) ( )
101
1 100
10
1 10 10
10
10 10
20
2 20
20
20 22
=
+ =
+
=
+
So, option (c) is correct.
8. The standard form of the number 12345 is
(a) 1234.5 × 10
1
(b) 123.45 × 10
2
(c) 12.345 × 10
3
(d) 1.2345 × 10
4
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 12345 = 1.2345 × 10
4
.
So, option (d) is correct.
9. If 2
1998
– 2
1997
– 2
1996
+ 2
1995
= K.2
1995
, then the value of K is
(a) 1 (b) 2 (c) 3 (d) 4
Solution:
( )
( )
3 2
1 2 4 8 2
1 2 2 2 2 2 2 2 2
1995
1995
1 2 3 1995 1995 1996 1997 1998
? =
+ - - =
+ - - = + - -
This implies, K = 3
So, option (c) is correct.
10. Which of the following is equal to 1?
(a) 2
0
+ 3
0
+ 4
0
(b) 2
0
× 3
0
× 4
0
(c) (3
0
– 2
0
) × 4
0
(d) (3
0
– 2
0
) × (3
0
+2
0
)
Solution:
2
0
× 3
0
× 4
0
= 1 × 1 × 1
= 1
So, option (b) is correct.
11. In standard form, the number 72105.4 is written as 7.21054 × 10
n
where
n is equal to
(a) 2 (b) 3 (c) 4 (d) 5
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 72105.4 = 7.21054 × 10
4
.
So, option (c) is correct.
12. Square of (-2/3) is
(a) -2/3 (b) 2/3 (c) -4/9 (d) 4/9
Solution:
9
4
3
2
3
2
3
2
2
=
?
?
?
?
?
?
- ? ?
?
?
?
?
?
- = ?
?
?
?
?
?
-
So, option (d) is correct.
13. Cube of (-1/4) is
(a) –1/12 (b) 1/16 (c) -1/64 (d) 1/64
Solution:
64
1
4
1
4
1
4
1
4
1
3
- =
?
?
?
?
?
?
- ? ?
?
?
?
?
?
- ? ?
?
?
?
?
?
- = ?
?
?
?
?
?
-
So, option (c) is correct.
14. Which of the following is not equal to (–5/4)
4
?
(a) (– 5)
4
/(4
4
) (b) (5
4
)/(– 4 )
4
(c) -(5
4
/ 4
4
) (d) (-5/4) x (-5/4) x (-5/4) x
(-5/4)
Solution:
4
5 5 5 5 5
4 4 4 4 4
625
256
? ? ? ? ? ? ? ? ? ?
- = - ? - ? - ? -
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
=
44
44
55
44
625
256
??
- = -
??
??
=-
So, option (c) is correct.
15. Which of the following is not equal to 1 ?
(a) (2
3
× 3
2
)/4 × 18 (b) [(-2)
3
× (-2)
4
] ÷ (-2)
7
(c) (3
0
× 5
3
)/(5×25) (d) 2
4
/(7
0
+ 3
0
)
3
Solution:
( )
( )
44
33
00
4
3
22
11
73
2
2
2
=
+
+
=
=
So, option (d) is correct.
16. (2/3)
3
× (5/7)
3
is equal to
(a) (2/3 × 5/7)
9
(b) (2/3 × 5/7)
6
(c) (2/3 × 5/7)
3
(d) (2/3 × 5/7)
0
Solution:
We know that, when power is same bases get multiplied in case of multiplication of
exponents, therefore,
3 3 3
2 5 2 5
3 7 3 7
? ? ? ? ? ?
? = ?
? ? ? ? ? ?
? ? ? ? ? ?
Sp, option (c) is correct.
17. In standard form, the number 829030000 is written as K × 10
8
where K
is equal to
(a) 82903 (b) 829.03 (c) 82.903 (d) 8.2903
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 829030000 = 8.2903 × 10 ^ 8
This implies, K is equal to 8.2903.
So, option (d) is correct.
18. Which of the following has the largest value?
(a) 0.0001 (b) 1/10000 (c) 1/10
6
(d) 1/10
6
÷ 0.1
Solution:
Among the given choices, 0.0001 has the largest value equivalent to 1×10
-4
.
So, option (a) is correct.
19. In standard form 72 crore is written as
(a) 72 × 10
7
(b) 72 × 10
8
(c) 7.2 × 10
8
(d) 7.2 × 10
7
Solution:
The standard exponential form is written as a a digit at once place followed by decimal and
the number of places the decimal is shifted towards left is raised to the power of 10.
Therefore, 72 crore is written as 7.2 × 10
8
.
So, option (c) is correct.
20. For non-zero numbers a and b, (a/b)
m
÷ (a/b)
n
, where m > n, is equal to
Solution:
We know that, when base is same power gets subtracted in case of division of exponents.
Therefore,
m n m n
a a a
b b b
-
? ? ? ? ? ?
?=
? ? ? ? ? ?
? ? ? ? ? ?
So, option (c) is correct.
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FAQs on NCERT Exemplar Solutions: Exponents & Powers - Mathematics (Maths) Class 7
| 1. How can exponents help simplify large numbers? |  |
Ans. Exponents help simplify large numbers by representing them in a shorter form. For example, 10^3 represents 10 multiplied by itself three times, which is 1000. This makes it easier to work with and compare large numbers.
| 2. What are the rules for multiplying and dividing numbers with exponents? | |
Ans. When multiplying numbers with exponents, you add the exponents if the base is the same. When dividing numbers with exponents, you subtract the exponents if the base is the same. For example, (a^2) * (a^3) = a^(2+3) = a^5 and (b^4) / (b^2) = b^(4-2) = b^2.
| 3. How do negative exponents work? | |
Ans. Negative exponents indicate that the base should be taken as the reciprocal. For example, a^-1 is equal to 1/a and b^-2 is equal to 1/(b^2). Negative exponents are used to represent fractions or decimals.
| 4. What is the power of a power rule in exponents? | |
Ans. The power of a power rule states that when you have an exponent raised to another exponent, you multiply the exponents. For example, (x^2)^3 = x^(2*3) = x^6. This rule helps simplify expressions with multiple exponents.
| 5. How can exponents be used in scientific notation? | |
Ans. Exponents are used in scientific notation to represent very large or very small numbers. In scientific notation, a number is written as a decimal between 1 and 10 multiplied by a power of 10. For example, 6.02 x 10^23 represents 6.02 multiplied by 10 raised to the 23rd power.
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