Class 7 Maths Chapter 10 Question Answers - Exponents and Powers

Q1. Express 16807 in exponential form.
Ans: Given: 16807
We need to express the given number in exponential form.
Exponential form is a way to represent a number in repeated multiplications of the same number.
So, we can write 16807 as
16807 = 7 × 7 × 7 × 7 × 7
16807 = 7⁵

Q2. Identify which is greater 2⁷ or 7².
Ans: Given: exponents 2⁷,7²
We need to find which exponent is greater.
We will find the value of each exponent and then compare it.
We can write the exponents as
2⁷ = 2 × 2 × 2 × 2 × 2 × 2 × 2
2⁷ = 128
7² = 7 × 7
7² = 49
Clearly, we can see that
2⁷>7²

Q3. Simplify 7³ × 2⁵.
Ans: Given: 7³ × 2⁵
We need to simplify the given exponential expression.
We can simplify the given expression as
7³ × 2⁵ = 7 × 7 × 7 × 2 × 2 × 2 × 2 × 2
7³ = 343 × 32
7³ = 10976

Q4. Write 1024 as a power of 2.
Ans: Given: 1024
We need to write the given expression as power of 2
Break 1024 in factors of 2 and write as exponents.
Therefore, 1024 as power of 2 will be written as
1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
⇒1024 = 2¹⁰

Q5.  Using laws, find the value of (3¹⁵ ÷ 3¹⁰) × 3².
Ans: Given: (3¹⁵ ÷ 3¹⁰) × 3²
We need to find the value of a given expression using laws.
We know that
a^m / aⁿ = a^{m − n}
a^m × aⁿ = a^m + n
Using these laws, the value of (3¹⁵ ÷ 3¹⁰) × 3² will be
= (3¹⁵ ÷ 3¹⁰) × 3²
= 3¹⁵ / 3¹⁰ × 3²
= 3^{15 − 10} × 3²
= 3⁵ × 3²
= 3^{5 + 2}
= 3⁷
= 2187

Q6. Find 8 × 10⁵ + 0 × 10⁴ + 3 × 10³ + 2 × 10² + 0 × 10¹ + 5 × 10⁰.
Ans: Given: 8 × 10⁵ + 0 × 10⁴ + 3 × 10³ + 2 × 10² + 0 × 10¹ + 5 × 10⁰
We need to find the value of the given expression.
We will solve the given exponents and then add them.
Therefore, the value of 8 × 10⁵ + 0 × 10⁴ + 3 × 10³ + 2 × 10²  + 0 × 10¹ + 5 × 10⁰  will be
= 8 × 100000 + 0000 + 3 × 1000 + 2 × 100 + 00 + 5 × 1
= 800000 + 0 + 3000 + 200 + 0 + 5
= 803205

Q7. Say True or False and Justify.
(a) 5² > 4³
Ans: Given: 5² > 4³
We need to find if the given expression is true or false.
We will solve the exponents and then compare them.
5² = 2⁵
4³ = 6⁴
25 < 64
⇒ 5² < 4³
Therefore, the expression is False.

(b) 5⁰ = 343⁰
Ans: Given: 5⁰ = 343⁰
We need to find if the given expression is true or false.
We will solve the exponents and then compare them.
5⁰ = 1
343⁰ = 1
∴ 5⁰ = 343⁰
Therefore, the expression is true.

Q8. Find the value of (3⁰ + 2⁰) × 5¹.
Ans: Given: (3⁰ + 2⁰) × 5¹
We need to find the value of a given expression.
We know that a⁰ = 1
Therefore, the value of (3⁰ + 2⁰) × 5¹ will be
= (3⁰ + 2⁰) × 5¹
= (1 + 1) × 5
= 2 × 5
= 10

Q9.  Find (a⁶ / a⁴) × a⁻² × a⁰ .
Ans: Given: (a⁶ / a⁴) × a⁻² × a⁰
We need to find the value of the given expression.
We know that
a^m / aⁿ = a^m−n
a^m × aⁿ = a^m+n
a⁰ = 1
Therefore, (a⁶ / a⁴) × a⁻² × a⁰  will be
=(a⁶⁻⁴) × a⁻² × a⁰
= a² × a⁻² × 1
= a²⁺⁽⁻²⁾
= a⁰
= 1

Q10. Find 27^p ÷ 27².
Ans: Given: 27^p ÷ 27²
We need to find the given expression.
We know that
a^m / aⁿ = a^m−n
Therefore, 27^p ÷ 27² will be
=(33)^p ÷ (33)²
=3^3p / 3⁶
=3^3p−6
=3^3(p−2)

Q11. Express each of the following as product of prime factor
(a) 702
Ans: We need to express the given expression as product of prime factor
Exponential form is a way to represent a number in repeated multiplications of the same number.
Therefore, 702 can be written as a product of prime factors as
702 = 2 × 3 × 3 x 3 × 13
= 2¹ × 3³ × 13¹

(b) 33275
Ans: Given: 33275
We need to express the given expression as a product of prime factors.
Exponential form is a way to represent a number in repeated multiplications of the same number.
Therefore, 33275  can be written as a product of prime factors as
33275 = 5 × 5 × 11 × 11 × 11
= 5² × 11³

Q12. Using the laws find
(a)
Ans:  Given:
We need to find the value of a given expression using laws.
We know that

Therefore, the value of  will be

(b)

Ans: Given:
We need to find the value of a given expression using laws.
We know that

Therefore, the value of  will be


Q13. Express each of the following as product of prime factors
(a) 729×625
Ans: We need to express the given expression as product of prime factor
Exponential form is a way to represent a number in repeated multiplications of the same number.
Therefore, 729×625 can be written as a product of prime factors as
729 = 3 × 3 × 3 × 3 × 3 × 3
= 3⁶
625 = 5 × 5 × 5 × 5
= 5⁴
∴ 729 × 625 = 3⁶ × 5⁴

(b)  1024×216
Ans: Given: 1024 × 216
We need to express the given expression as a product of prime factors.
Exponential form is a way to represent a number in repeated multiplications of the same number.
Therefore, 1024×216 can be written as a product of prime factors as
1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2¹⁰
216 = 2 × 2 × 2 × 3 × 3 × 3 = 2³ × 3³
∴ 1024 × 216 = 2¹⁰ ×  2³ × 3³
= 2^{10 + 3} × 3³
= 2¹³ × 3³

Q14. Express the following as standard form
(a) 3,68,878
Ans: Given: 3,68,878
We need to express the given number as a standard form.
We will write the given numbers as a multiple of power of 10.
Therefore, the standard form of 3,68,878  will be
=3.68878 × 100000
=3.68878 × 10⁵

(b) 4,78,25,00,000
Ans: Given: 4,78,25,00,000
We need to express the given number as a standard form.
We will write the given numbers as a multiple of power of 10.
Therefore, the standard form of 4,78,25,00,000 will be
=4.7825 × 1000000000
=4.7825 × 10⁹