NCERT Solutions for Class 7 Maths Exercise 13.1

NCERT Solutions for Class 7 Maths Exercise 13.1 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 7 Maths chapter wise NCERT solution for Maths Book all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Maths Exponents and Powers Download as PDF

NCERT Solutions for Class 7 Maths Exponents and Powers

Class –VII Mathematics (Ex. 13.1)

Question 1.Find the value of:

(i){tex}{2^6}{/tex}

(ii){tex}{9^3}{/tex}

(iii){tex}{11^2}{/tex}

(iv) {tex}{5^4}{/tex}

Answer:

(i) {tex}{2^6}{/tex}= 2 x 2 x 2 x 2 x 2 x 2 = 64

(ii) {tex}{9^3}{/tex}= 9 x 9 x 9 = 729

(iii) {tex}{11^2}{/tex}= 11 x 11 = 121

(iv) {tex}{5^4}{/tex}= 5 x 5 x 5 x 5 = 625

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NCERT Solutions for Class 7 Maths Exercise 13.1

Question 2.Express the following in exponential form:

(i) 6 x 6 x 6 x 6

(ii) {tex}t \times t{/tex}

(iii) {tex}b \times b \times b \times b{/tex}

(iv) 5 x 5 x 7 x 7 x 7

(v) {tex}2 \times 2 \times a \times a{/tex}

(vi) {tex}a \times a \times a \times c \times c \times c \times c \times d{/tex}

Answer:

(i) 6 x 6 x 6 x 6 = {tex}{6^4}{/tex}

(ii) {tex}t \times t = {t^2}{/tex}

(iii) {tex}b \times b \times b \times b = {b^4}{/tex}

(iv) 5 x 5 x 7 x 7 x 7 = 52 x 73

(v) {tex}2 \times 2 \times a \times a = {2^2} \times {a^2}{/tex}

(vi) {tex}a \times a \times a \times c \times c \times c \times c \times d = {a^3} \times {c^4} \times d{/tex}

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NCERT Solutions for Class 7 Maths Exercise 13.1

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

(i) 512

(ii) 343

(iii) 729

(iv) 3125

Answer:

(i) 512

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = {tex}{2^9}{/tex}

(ii) 343

= 7 x 7 x 7 = {tex}{7^3}{/tex}

(iii) 729

= 3 x 3 x 3 x 3 x 3 x 3 = {tex}{3^6}{/tex}

(iv) 3125

=5x5x5x5x5 = {tex}{5^5}{/tex}

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NCERT Solutions for Class 7 Maths Exercise 13.1

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

(i) {tex}{4^3}{/tex}and{tex}{3^4}{/tex}

(ii) {tex}{5^3}{/tex}or {tex}{3^5}{/tex}

(iii) {tex}{2^8}{/tex}or{tex}{8^2}{/tex}

(iv) {tex}{100^2}{/tex}or {tex}{2^{100}}{/tex}

(v) {tex}{2^{10}}{/tex}or{tex}\;{10^2}{/tex}

Answer:

(i) {tex}{4^3}{/tex}= 4 x 4 x 4 = 64

{tex}{3^4}{/tex}= 3 x 3 x 3 x 3 = 81

Since 64 < 81

Thus, {tex}{3^4}{/tex}is greater than {tex}{4^3}{/tex}.

(ii) {tex}{5^3}{/tex}= 5 x 5 x 5 = 125

{tex}{3^5}{/tex}= 3 x 3 x 3 x 3 x 3 = 243

Since, 125 < 243

Thus, {tex}{3^4}{/tex}is greater than {tex}{5^3}{/tex}.

(iii) {tex}{2^8}{/tex}= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256

{tex}{8^2}{/tex}= 8 x 8 = 64

Since, 256 > 64

Thus, {tex}{2^8}{/tex}is greater than{tex}{8^2}{/tex}.

(iv) {tex}{100^2}{/tex}= 100 x 100 = 10,000

{tex}{2^{100}}{/tex}= 2 x 2 x 2 x 2 x 2 x …..14 times x ……… x 2 = 16,384 x ….. x 2

Since, 10,000 < 16,384 x ……. X 2

Thus, {tex}{2^{100}}{/tex}is greater than{tex}{100^2}{/tex}.

(v) {tex}{2^{10}}{/tex}= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1,024

{tex}{10^2}{/tex}= 10 x 10 = 100

Since, 1,024 > 100

Thus, {tex}{2^{10}}{/tex}> {tex}{10^2}{/tex}

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NCERT Solutions for Class 7 Maths Exercise 13.1

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

(i) 648

(ii) 405

(iii) 540

(iv) 3,600

Answer:

(i) 648 = {tex}{2^3} \times {3^4}{/tex}

(ii) 405 = {tex}5 \times {3^4}{/tex}

(iii) 540 = {tex}{2^2} \times {3^3} \times 5{/tex}

(iv) 3,600 = {tex}{2^4} \times {3^2} \times {5^2}{/tex}

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NCERT Solutions for Class 7 Maths Exercise 13.1

Question 6.Simplify:

(i){tex}2 \times {10^3}{/tex}

(ii) {tex}{7^2} \times {2^2}{/tex}

(iii){tex}{2^3} \times 5{/tex}

(iv) {tex}3 \times {4^4}{/tex}

(v){tex}0 \times {10^2}{/tex}

(vi) {tex}{5^2} \times {3^3}{/tex}

(vii){tex}{2^4} \times {63^2}{/tex}

(viii) {tex}{3^2} \times {10^4}{/tex}

Answer:

(i) {tex}2 \times {10^3}{/tex}= 2 x 10 x 10 x 10 = 2,000

(ii) {tex}{7^2} \times {2^2}{/tex}= 7 x 7 x 2 x 2 = 196

(iii) {tex}{2^3} \times 5{/tex}= 2 x 2 x 2 x 5 = 40

(iv) {tex}3 \times {4^4}{/tex}= 3 x 4 x 4 x 4 x 4 = 768

(v) {tex}0 \times {10^2}{/tex}= 0 x 10 x 10 = 0

(vi) {tex}{5^2} \times {3^3}{/tex}= 5 x 5 x 3 x 3 x 3 = 675

(vii) {tex}{2^4} \times {63^2}{/tex}= 2 x 2 x 2 x 2 x 3 x 3 = 144

(viii) {tex}{3^2} \times {10^4}{/tex}= 3 x 3 x 10 x 10 x 10 x 10 = 90,000

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NCERT Solutions for Class 7 Maths Exercise 13.1

Question 7.Simplify:

(i) {tex}{\left( { – 4} \right)^3}{/tex}

(ii) {tex}\left( { – 3} \right) \times {\left( { – 2} \right)^3}{/tex}

(iii) {tex}{\left( { – 3} \right)^2} \times {\left( { – 5} \right)^2}{/tex}

(iv) {tex}{\left( { – 2} \right)^3} \times {\left( { – 10} \right)^3}{/tex}

Answer:

(i) {tex}{\left( { – 4} \right)^3} = \left( { – 4} \right) \times \left( { – 4} \right) \times \left( { – 4} \right) = – 64{/tex}

(ii) {tex}\left( { – 3} \right) \times {\left( { – 2} \right)^3} = \left( { – 3} \right) \times \left( { – 2} \right) \times \left( { – 2} \right) \times \left( { – 2} \right) = 24{/tex}

(iii) {tex}{\left( { – 3} \right)^2} \times {\left( { – 5} \right)^2} = \left( { – 3} \right) \times \left( { – 3} \right) \times \left( { – 5} \right) \times \left( { – 5} \right) = 225{/tex}

(iv) {tex}{\left( { – 2} \right)^3} \times {\left( { – 10} \right)^3} = \left( { – 2} \right) \times \left( { – 2} \right) \times \left( { – 2} \right) \times \left( { – 10} \right) \times \left( { – 10} \right) \times \left( { – 10} \right){/tex}

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NCERT Solutions for Class 7 Maths Exercise 13.1

Question 8.Compare the following numbers:

(i) {tex}2.7 \times {10^{12}}{/tex};{tex}1.5{\text{ }}x{\text{ }}{10^8}{/tex}

(ii) {tex}4 \times {10^{14}}{/tex}; {tex}3 \times {10^{17}}{/tex}

Answer:

(i) {tex}2.7 \times {10^{12}}{/tex}and {tex}1.5{\text{ }}x{\text{ }}{10^8}{/tex}

On comparing the exponents of base 10,

{tex}2.7 \times {10^{12}}{/tex}> {tex}1.5{\text{ }}x{\text{ }}{10^8}{/tex}

(ii) {tex}4 \times {10^{14}}{/tex}and {tex}3 \times {10^{17}}{/tex}

On comparing the exponents of base 10,

{tex}4 \times {10^{14}}{/tex}< {tex}3 \times {10^{17}}{/tex}

NCERT Solutions for Class 7 Maths Exercise 13.1

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