CBSE Class 7 Mathematics Exponents And Powers Worksheet Set 01

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

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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 = __

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