Class 7 Exponents and Powers Ex 11.1

NCERT Solutions For Class 7 Maths Chapter 11 – Exponents and Powers

Simple solutions for NCERT Solutions for Class 7 Maths Exercise 11.1 Chapter 11 Exponents and Powers are given here in the post. This NCERT Solutions for Class 7 Maths Exercise 11.1 contains topics related to the raw data collection and its organisation. so we definitely want students of Class 7 to solve Class 7 Exponents and Powers NCERT Exercise 11.1 to empower their basics and test the students capability of understanding the concepts. It also helps the students of CBSE Class 7 Maths students

Question 1. Find the value of:

(i) \(2^6= 2 × 2 × 2 × 2 × 2 × 2 = 64\)

(ii) \(9^3=9 × 9 × 9 = 729\)

(iii) \(11^2=11 × 11 = 121\)

(iv) \(5^4= 5 × 5 × 5 × 5 = 625\)

Question 2. Express the following in exponential form:

(i) \(6 × 6 × 6 × 6 = 6^4\)

(ii)\(t × t = t^2\)

(iii) \(b × b × b × b = b^4\)

(iv) \(5 × 5× 7 × 7 × 7 = 5^2 × 7^3\)

(v) \(2 × 2 × a × a = 2^2 × a^2\)

(vi) \(a × a × a × c × c × c × c × d = a^3 × c^4 × d\)

Question 3. Express each of the following numbers using exponential notation:

(i) \(512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^9\)

(ii) \(343 = 7 × 7 × 7= 7^3\)

(iii) \(729 = 3 × 3 × 3 × 3 × 3 × 3= 3^6\).

(iv) \(3125 = 5 × 5 × 5 × 5 × 5= 5^5\).

Question 4. Identify the greater number, wherever possible, in each of the following?

(i)\( 4^3  \ or \  3^4\)

Solution:-

The expansion of \(4^3 = 4 × 4 × 4 = 64\)

The expansion of \(3^4 = 3 × 3 × 3 × 3 = 81\)

\(64 < 81\)

So, \(4^3 < 3^4\)

Hence \(3^4\) is the greater number.

(ii) \(5^3  \ or \  3^5\)

Solution:-

The expansion of \(5^3 = 5 × 5 × 5 = 125\)

The expansion of \(3^5 = 3 × 3 × 3 × 3 × 3= 243\)

\(125 < 243\)

So, \(5^3 < 3^5 \)

Hence 35 is the greater number.

(iii) \(2^8  \ or \ 8^2\)

Solution:-

The expansion of \(2^8 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256\)

The expansion of \(8^2 = 8 × 8= 64\)

Clearly,

\(256 > 64\)

So, \(2^8 > 82\)

Hence \(2^8\) is the greater number.

(iv) \(100^2 \ or \ 2100\)

Solution:-

The expansion of \(100^2 = 100 × 100 = 10000\)

The expansion of \(2^{10} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024\)

\((2^{10})^{10}= 1024 × 1024 ×1024 × 1024 ×1024 × 1024 × 1024 × 1024 × 1024 × 1024\)

Clearly,

\(100^2 < 2^{100}\)

Hence \(2^{100}\) is the greater number.

(v) \(2^{10}  \ or \  10^2\)

Solution:-

The expansion of  \(2^{10} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024\)

The expansion of \(10^2= 10 × 10= 100\)

Clearly,

\(1024 > 100\)

So, \(2^{10} > 10^2\)

Hence \(2^{10}\) is the greater number.

Question 5. Express each of the following as product of powers of their prime factors:

(i) \(648\)

Solution:-

Factors of \(648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2^3 × 3^4\)

(ii) \(405\)

Solution:-

Factors of \(405 = 3 × 3 × 3 × 3 × 5= 3^4 × 5\)

(iii) \(540\)

Solution:-

Factors of \(540 = 2 × 2 × 3 × 3 × 3 × 5 = 2^2× 3^3× 5\)

(iv) \(3,600\)

Solution:-

Factors of \(3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 2^4× 3^2× 5^2\)

Question 6. Simplify:

(i) \(2 × 10^3\)

Solution:-

\(2 × 10^3 = 2 × 10 × 10 × 10\)

\(= 2 × 1000\)

\(= 2000\)

(ii) \(7^2 × 2^2\)

Solution:-

\(7^2 × 2^2 = 7 × 7 × 2 × 2\)

\(= 49 × 4\)

\(= 196\)

(iii) \(2^3× 5\)

Solution:-

\(2^3× 5 = 2 × 2 × 2 × 5\)

\(= 8 × 5\)

\(= 40\)

(iv) \(3 × 4^4\)

Solution:-

\(3 × 4^4 = 3 × 4 × 4 × 4 × 4\)

\(= 3 × 256\)

\(= 768\)

(v) \(0 × 10^2\)

Solution:-

\(0 × 10^2 = 0 × 10 × 10\)

\(= 0 × 100\)

\(= 0\)

(vi) \(5^2 × 3^3\)

Solution:-

\(5^2 × 3^3 = 5 × 5 × 3 × 3 × 3\)

\(= 25 × 27\)

\(= 675\)

(vii) \(2^4 × 3^2\)

Solution:-

\(2^4 × 3^2 = 2 × 2 × 2 × 2 × 3 × 3\)

\(= 16 × 9\)

\(= 144\)

(viii) \(3^2 × 10^4\)

Solution:-

\(3^2 × 10^4= 3 × 3 × 10 × 10 × 10 × 10\)

\(= 9 × 10000\)

\(= 90000\)

Question 7. Simplify:

(i) \((– 4)^3\)

Solution:-

The expansion of \((– 4)^3\)

\(= – 4 × – 4 × – 4= – 64\)

(ii) \((–3) × (–2)^3\)

Solution:-

The expansion of \((–3) × (–2)^3\)

\(= – 3 × – 2 × – 2 × – 2\)

\(= – 3 × – 8\)

\(= 24\)

(iii) \((–3)^2 × (–5)^2\)

Solution:-

The expansion of \((–3)^2 × (–5)^2\)

\(= – 3 × – 3 × – 5 × – 5\)

\(= 9 × 25\)

\(= 225\)

(iv) \((–2)^3 × (–10)^3\)

Solution:-

The expansion of \((–2)^3 × (–10)^3\)

\(= – 2 × – 2 × – 2 × – 10 × – 10 × – 10\)

\(= – 8 × – 1000\)

\(= 8000\)

Question 8. Compare the following numbers:

(i)\(2.7 × 10^{12} ; 1.5 × 10^8\)

Solution:-

Comparing the exponents of base 10,

\(2.7 × 10^{12} > 1.5 × 10^8\)

(ii) \(4 × 10^{14} ; 3 × 10^{17}\)

Solution:-

By observing the question

Comparing the exponents of base 10,

Clearly,\(4 × 10^{14} < 3 × 10^{17}\)