CBSE Class 7 Mathematics Exponents And Powers Worksheet Set A

CBSE Clas 7 Maths Worksheet - Exponents & Powers (1)

Worksheets have become an integral part of the education system. Worksheets are very critical for every student to practice his/ her concepts. Students, teachers and parents can download all CBSE educational material and extremely well prepared worksheets from this website. All revision worksheets, Sample papers, Question banks and easy to learn study notes for all classes and subjects have been prepared based on the latest guidelines sent by CBSE. All CBSE educational material is developed by our panel of teachers, have also been submitted by thousands of teachers and students. The study material has been carefully compiled by the best teachers in India. Worksheets have been submitted by teachers of various CBSE schools and also have been carefully developed keeping into consideration the latest CBSE syllabus.

1. Write each of the following in power notation:

(i) (5/7) ×(5/7) × (5/7) × (5/7)
Solution:-
The product of rational number multiplied several times by itself can be expressed in the power notations as,
(5/7)⁴

(ii) (-4/3) ×(-4/3) × (-4/3) × (-4/3) × (-4/3)
Solution:-
The product of rational number multiplied several times by itself can be expressed in the power notations as,
(-4/3)⁵

2. Express each of the following in power notation:

(i) (25/36)
Solution:-
We have,
25 = 5 × 5 = (5)²
36 = 6 × 6 = (6)²
Then,
= (5²/6²)
∴ (5/6)²

(ii)(-27/64)
Solution:-
We have,
-27 = -3 × -3 × -3 = (-3)³
64 = 4 × 4 × 4 = (4)³
Then,
= (-3³/4³)
∴ (-3/4)³

3. Express each of the following a rational number:
(i) (-8/5)³
Solution:-
We have,
(-8/5)³ = (-8³/5³)
= (-8 × -8 × -8) / (5 × 5 × 5)
= (-512/125)

(ii) (-13/11)²
Solution:-
We have,
(-13/11)² = (-13²/11²)
= (-13 × -13) / (11 × 11)
= (169/121)

4. Express each of the following as a rational number:

(i) (4)^-1
Solution:-
We have:
(4)^-1 = (4/1)^-1
= (1/4)¹ … [∵ (a/b)^-n = (b/a) ⁿ]
= (1/4)

(ii) (-6)^-1
Solution:-
We have:
(-6)^-1 = (-6/1)^-1
= (1/-6)¹ … [∵ (a/b)^-n = (b/a) ⁿ]
= (-1/6)

5. Find the reciprocal of each of the following:
(i) (3/8)⁴
Solution:-
We know that the reciprocal of (a/b) ^m is (b/a) ^m
Then,
Reciprocal of (3/8)⁴ is (8/3)⁴

(ii) (-5/6)¹¹
Solution:-
We know that the reciprocal of (a/b) ^m is (b/a) ^m
Then,
Reciprocal of (-5/6)¹¹ is (-6/5)¹¹

6. Find the value of each of the following:

(i) 8⁰
Solution:-
By definition, we have a0= 1 for every integer.
∴ 8⁰ = 1

(ii) 6⁰ × 7⁰
Solution:-
By definition, we have a⁰= 1 for every integer.
∴ 6⁰ × 7⁰
= 1 × 1
= 1

7. Simplify each of the following and express each as a rational number:

(i) (3/2)⁴ × (1/5)²
Solution:-
We have,
(3⁴/2⁴) = (3×3×3×3)/ (2×2×2×2) = (81/16)
(1²/5²) = (1×1)/ (5×5) = (1/25)
Then,
= (81/16) × (1/25)
= (81×1) / (16/25)
= (81/400)

(ii) (-2/3)⁵ × (-3/7)³
Solution:-
We have,
(-2⁵/3⁵) = (-2×-2×-2×-2×-2)/ (3×3×3×3×3) = (-32/243)
(-3³/7³) = (-3×-3×-3)/ (7×7×7) = (-27/343)
Then,
= (-32/243) × (-27/343)
= (-32×-27) / (243×343)
By simplifying,
= (-32×-1) / (9/343)
= (32/3087)

8. Simplify and express each as a rational number:

(i) (4/9)⁶× (4/9)^-4
Solution:-
We have,
= (4/9) ^{(6+ (-4))} … [{(a/b) ^m × (a/b) ⁿ} = (a/b)^m-n
= (4/9) ^(6-4)
= (4/9)²
= (4²/9²)
= (16/81)

(ii) (-7/8)^-3× (-7/8)²
Solution:-
We have,
= (-7/8) ^{(-3+ 2)} … [{(a/b) ^m × (a/b) ⁿ} = (a/b)^m-n
= (-7/8) ^(-1)
= (-8/7)

9. Express each of the following as a rational number:

(i) 5^-3
Solution:-
We know that,
= (5)^-3 = (1/5)³ … [∵ (a/b)^-n = (b/a) ⁿ]
= (1³/5³)
= (1/125)

(ii) (-2)^-5
Solution:-
We know that,
= (-2)^-5 = (-1/2)³ … [∵ (a/b)^-n = (b/a) ⁿ]
= (-1³/2³)
= (-1/8)

More QUestion

1. Find the value of the following:

a) 82
b) 63
c) 26
d) 112
e) 54
f) 25
g) (–4)³
h) (–5)⁴

2. Write in exponential form.

a) 5 × 5 × 5 × 5 × 5 = ____________
b) (–4) × (–4) × (–4) = ____________
c) 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = ____________
d) (–8) × (–8) × (–8) × (–8) = ____________
e) 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = __

Please click the below link to access CBSE Clas 7 Maths Worksheet - Exponents & Powers (1)