Short and Long Question: Exponents And Powers | Short & Long Answer Questions for Class 7 PDF Download

Q1: Can you find two integers m,n such that 2^m+n = 2^mn ?
Ans: Equating the powers of 2^m+n =2^mn  that is m+n = mn.
Now we have to find such integers so that the sum of the integers is equal to their product and those integers are 0 and 2:
Let us first take m=2 and n=2, we get
2 + 2 = 2 × 2
⇒ 4 = 4
which is true
Now take m=0 and n=0, we get
0 + 0 = 0 × 0
⇒ 0 = 0
which is true
Hence the integers are m = 0, 2 and n = 0, 2.

Q2: Simplify the following using laws of indices:

Ans: The given expression  can be simplified as follows:

Hence  = 12^1/4

Q3: Evaluate
(i) 2^-2
(ii) (-2)^-2
(iii) (3/2)^-5
Ans: As we know that
b^-n = 1/bn
(i) 2^-2 = 1/ 2² = 1/4
(ii) (-2)^-2 = 1/(-2)² = 1/4
(iii) (3/2)^-5 = 3^-5/ 2^-5 =2⁵/3⁵ = 32/243

Q4: Simplify and express the result in power notation with positive exponent.
(i) (-2)⁵ ÷ (-2)⁴
(ii) (1/2)² × (2/5)²
(iii) (-5)² × (3/5)
Ans: 
(i) (-2)⁵ ÷ (-2)⁴
= (-2)⁵ / (-2)⁴
= (-2)^5-4
=-2
(ii) (1/2)² × (2/5)²
= (1/4) X (4/25)
= 1/25
(iii) (-5)² × (3/5)
=25 × (3/5) =15

Q5: Express the following numbers in standard form.
(i) 0.0000000015
(ii) 0.00000001425
Ans:
(i) 0.0000000015
=1.5 ×10^-9
(ii) 0.00000001425
=1.425×10^-8
(iii) 102000000000000000
=1.02×10¹⁷

Q6: Simplify the following:
(i) 10³ × 9⁰ + 3³ × 2 + 7⁰
(ii) 6³ × 7⁰ + (-3)⁴ – 9⁰
Ans:
(i) 10³ × 9⁰ + 3³ × 2 + 7⁰
= 1000 + 54 + 1
= 1055
(ii) 6³ × 7⁰ + (-3)⁴ – 9⁰
= 216 × 1 + 81 – 1
= 216 + 80
= 296

Q7: Write the following in expanded form:
(i) 70,824
(ii) 1,69,835
Ans:
(i) 70,824
= 7 × 10000 + 0 × 1000 + 8 × 100 + 2 × 10 + 4 × 10⁰
= 7 × 10⁴ + 8 × 10² + 2 × 10¹ + 4 × 100
(ii) 1,69,835= 1 × 100000 + 6 × 10000 + 9 × 1000 + 8 × 100 + 3 × 10 + 5 × 100
= 1 × 10⁵ + 6 × 10⁴ + 9 × 10³ + 8 × 10² + 3 × 10¹ + 5 × 10⁰

Q8: Find the number from each of the expanded form:
(i) 7 × 10⁸ + 3 × 10⁵ + 7 × 10² + 6 × 10¹ + 9
(ii) 4 × 107 + 6 × 103 + 5
Ans:
(i) 7 × 108 + 3 × 10⁵ + 7 × 10² + 6 × 10¹ + 9
= 7 × 100000000 + 3 × 100000 + 7 × 100 + 6 × 10 + 9
= 700000000 + 300000 + 700 + 60 + 9
= 700300769
(ii) 4 × 10⁷ + 6 × 10³ + 5
= 4 × 10000000 + 6 × 1000 + 5
= 40000000 + 6000 + 5
= 40006005

Q9: Express the following in standard form:
(i) 8,19,00,000
(ii) 5,94,00,00,00,000
(iii) 6892.25
Ans:
(i) 8,19,00,000 = 8.19 × 10⁷
(ii) 5,94,00,00,00,000 = 5.94 × 10¹¹
(iii) 6892.25 = 6.89225 × 10³

Q10: 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
Ans: :
(i) 5 × 5 × 5 × 5 × 5 = (5)⁵
(ii) 4 × 4 × 4 × 5 × 5 × 5 = 4³ × 5³
(iii) (-1) × (-1) × (-1) × (-1) × (-1) = (-1)⁵
(iv) a × a × a × b × c × c × c × d × d = a³b¹c³d²