NCERT Solutions for Class 7 Maths Exercise 13.1

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NCERT solutions for Maths Exponents and Powers Download as PDF

NCERT Solutions for Class 7 Maths Exercise 13.1

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


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}


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}


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}


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}


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


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}


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

NCERT Solutions Class 7 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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