NCERT Solutions for Class 7 Maths Chapter 11 Exponents and Powers

NCERT Solutions for Class 7 Maths Chapter 11 Exponents and Powers - Important Points

Exponents: Exponents represent repeated multiplication of a number (base) by itself.

For $\mathrm{x}^4$ where x is the base, and 4 is the exponent. It is read as x raised to the power of 4 or the fourth power of $x$.

Understanding Powers of 10:

• Powers of 10 are commonly used in scientific notation and decimal places.
• $10^n$ represents a 1 followed by 'n' zeros.

Law of Exponents

$a^m \times a^n=a^{(m+n)}$

$\frac{a^m}{a^n}=a^{(m-n)}$

$\left(a^m\right)^n=a^{\left(mn\right)}$

$(a b)^n=a^{n} b^n$

$(\frac{a}{b})^m= \frac{a^m}{b^m}$

$a^{0} = 1$

$
(-)^{\text {even number }}=1
$

$
(-)^{\text {odd number }}=-1
$

NCERT Solutions for Maths Chapter 11 Class 7 - Download PDF

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NCERT Solutions for Class 7 Maths Exponents and Powers - Exercise

Question: 1(i) Find the value of:

$(i)2^{6}$

Answer:

The value of $2^6$ is given by

$2\times 2\times2 \times 2\times2 \times 2=64$

Question: 1(ii) Find the value of:

$(ii)9^{3}$

Answer:

The value of $9^{3}$ is given by

$9\times 9\times 9=729$

Question: 1(iii) Find the value of:

$(iii)11^{2}$

Answer:

The value of $11^{2}$ is given by

$11\times 11=121$

Question: 1(iv) Find the value of:

$(iv)5^{4}$

Answer:

The value of $5^{4}$ is given by

$5^4=5\times 5\times 5\times 5=625$

Question: 2 Express the following in exponential form:

$(i)6\times 6\times 6\times 6$

$(ii)t\times t$

$(iii)b\times b\times b\times b$

$(iv)5\times 5\times 7\times 7\times 7$

$(v)2\times 2\times a\times a$

$(vi)a\times a\times a\times c\times c\times c\times c\times d$

Answer:

$(i)6\times 6\times 6\times 6$ can be given as

$6^4$ .

$(ii)t\times t$ can be given as $t^2$ .

$(iii)b\times b\times b\times b$ can be given as $b^4$ .

$(iv)5\times 5\times 7\times 7\times 7$ can be given as

$5^2\times 7^3$ .

$(v)2\times 2\times a\times a$ can be given as

$2^2\times a^2$ .

$(vi)a\times a\times a\times c\times c\times c\times c\times d$ can be given as

$a^3\times c^4\times d$ .

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

(i) 512 (ii) 343 (iii) 729 (iv) 3125

Answer:

(i) 512

$512=2\times 2\times2 \times2 \times 2\times 2\times2 \times 2\times 2=2^9$

(ii) 343

$343=7\times 7\times 7=7^3$

(iii)729

$729=3\times 3\times 3\times 3\times 3\times 3=3^6$

(iv)3125

$3125=5\times 5\times 5\times 5\times 5=5^5$

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

$(i)4^{3}or \: 3^{4}$
$(ii) 5^{3}or \: 3^{5}$
$(iii) 2^{8}or \: 8^{2}$
$(iv) 100^{2}or \: 2^{100}$
$(v) 2^{10}or \: 10^{2}$

Answer:

$(i)4^{3}or \: 3^{4}$

$4^3=4\times 4\times 4=64$

$3^4=3\times 3\times 3\times 3=81$

since $81> 64$

$3^4$ is greater than $4^3$

$(ii) 5^{3}or \: 3^{5}$

$5^3=5\times 5\times 5=125$

$3^5=3\times 3\times 3\times 3\times 3=243$

since $243> 125$

$3^5$ is greater than $5^3$

$(iii) 2^{8}or \: 8^{2}$

$2^8=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=256$

$8^2=8\times 8=64$

since $256 > 64$

$2^8$ is greater than $8^2$

$(iv) 100^{2}or \: 2^{100}$

$100^2=100\times 100=10000$

$2^{100}=2 \times 2 \times 2 \times 2 \times 2$ till 100 times 2 since $2^{100}>100^2$
$2^{100}$ is greater than $100^2$

$(v) 2^{10}or \: 10^{2}$

$2^10=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=1024$

$10^2=10\times 10=100$

since $1024> 100$

$2^10$ is greater than $10^2$

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

(i) 648 (ii) 405 (iii) 540 (iv) 3,600

Answer:

(i) 648

$648=2^3\times 3^4$

(ii) 405

$405=5\times 3^4$

(iii)540

$540=2^2\times 3^3\times 5$

(iv) 3600

$3600=2^4\times 3^2\times 5 ^2$

Question: 6(i) Simplify:

$(i)2\times 10^{3}$

Answer:

$(i)2\times 10^{3}$

can be simplified as

$2\times 10\times 10\times 10=2000$

Question: 6(ii) Simplify:

$(ii)7^{2}\times 2^{2}$

Answer:

$(ii)7^{2}\times 2^{2}$

can be simplified as

$7\times 7\times 2\times 2=196$

Question: 6(iii) Simplify:

$(iii) 2^{3}\times 5$

Answer:

$(iii) 2^{3}\times 5$

can be simplified as

$2\times 2\times 2\times 5=40$

Question: 6(iv) Simplify:

$(iv) 3\times 4^{4}$

Answer:

$(iv) 3\times 4^{4}$

can be simplified as

$3 \times 4\times 4\times 4\times 4=768$

Question: 6(v) Simplify:

$(v)0\times 10^{2}$

Answer:

$(v)0\times 10^{2}$

can be simplified as

$0\times 10\times 10=0$

Question: 6(vi) Simplify:

$(vi)5^{2}\times 3^{3}$

Answer:

$(vi)5^{2}\times 3^{3}$

can be simplified as

$5\times 5\times 3\times3 \times 3=675$

Question: 6(vii) Simplify:

$(vii) 2^{4}\times 3^{2}$

Answer:

$(vii) 2^{4}\times 3^{2}$

can be simplified as

$2\times 2\times 2\times 2\times 3\times 3=144$

Question: 6(viii) Simplify:

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

Answer:

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

can be simplified as

$3\times3 \times 10\times 10\times10 \times 10=90000$

Question: 7(i) Simplify:

$(i)(-4)^{3}$

Answer:

$(i)(-4)^{3}$

can be simplified as

$-4\times -4\times -4=-64$

Question: 7(ii) Simplify:

$(ii) (-3)\times (-2)^{3}$

Answer:

$(ii) (-3)\times (-2)^{3}$

can be simplified as

$-3\times -2\times -2\times -2=24$

Question: 7(iii) Simplify:

$(iii) (-3)^{2}\times (-5)^{2}$

Answer:

$(iii) (-3)^{2}\times (-5)^{2}$

can be simplified as

$(-3)\times (-3)\times (-5)\times (-5)=225$

Question: 7(iv) Simplify:

$(iv) (-2)^{3}\times (-10)^{3}$

Answer:

$(iv) (-2)^{3}\times (-10)^{3}$

can be simplified as

$(-2)\times (-2)\times (-2)\times- 10\times -10\times -10=8000$

Question: 8 Compare the following numbers:

$(i) 2.7\times 10^{12} ;1.5\times 10^{8}$ $(ii) 4\times 10^{14} ;3\times 10^{17}$

Answer:

$(i) 2.7\times 10^{12} ;1.5\times 10^{8}$

on comparing exponents of base 10.

$2.7\times 10^{12} > 1.5\times 10^{8}$

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

on comparing exponents of base 10.

$4\times 10^{14} < 3\times 10^{17}$

Question: 1 Using laws of exponents, simplify and write the answer in exponential form:

$(i)\: 3^{2}\times 3^{4}\times 3^{8}$

$(ii)\: 6^{15}\div 6^{10}$

$(iii)\: a^{3}\times a^{2}$

$(iv)\: 7^{x}\times 7^{2}$

$(v)\:(5^{2})^{3}\div 5^{3}$

$(vi)\:2^{5}\times 5^{5}$

$(vii)\:a^{4}\times b^{4}$

$(viii)\:(3^{4})^{3}$

$(ix)\:(2^{20}\div 2^{15})\times 2^{3}$

$(x)\:8^{t}\div 8^{2}$

Answer:

$(i)\: 3^{2}\times 3^{4}\times 3^{8}$

can be simplified as $3^{(2+4+8)}=3^{14}$

$(ii)\: 6^{15}\div 6^{10}$

can be simplified as $6^{(15-10)}=6^{5}$

$(iii)\: a^{3}\times a^{2}$

can be simplified as $a^{(3+2)}=a^{5}$

$(iv)\: 7^{x}\times 7^{2}$

can be simplified as $7^{(x+2)}=7^{(x+2)}$

$(v)\:(5^{2})^{3}\div 5^{3}$

can be simplified as
$5^{(2\times 3)}\div 5^{(3)}=5^6\div 5^3=5^{6-3}=5^3$

$(vi)\:2^{5}\times 5^{5}$

can be simplified as

$(2\times5)^{5}=10^5$

$(vii)\:a^{4}\times b^{4}$

can be simplified as $(ab)^4$

$(viii)\:(3^{4})^{3}$

can be simplified as $3^{4\times 3}=3^{12}$

$(ix)\:(2^{20}\div 2^{15})\times 2^{3}$

can be simplified as
$2^{(20-15)}\times 2^3=2^5\times 2^3=2^{(5+3)}=2^8$

$(x)\:8^{t}\div 8^{2}$

can be simplified as $8^{(t-2)}$

Question: 2(i) Simplify and express each of the following in exponential form:

$(i)\: \frac{2^{3}\times 3^{4}\times 4}{3\times 32}$

Answer:

$(i)\: \frac{2^{3}\times 3^{4}\times 4}{3\times 32}$

can be simplified as

$=\frac{2^3\times 3^4\times 2^2}{3\times 2^5}$

$=\frac{ 2^{(3+2)} \times 3^4}{3\times 2^5}$

$=\frac{ 2^{5} \times 3^4}{3\times 2^5}$

$= 2^{(5-5)} \times 3^{(4-1)}$

$=3^3$

Question: 2(ii) Simplify and express each of the following in exponential form:

$(ii)\: ((5^{2})^{3}\times 5^{4})\div 5^{7}$

Answer:

$(ii)\: ((5^{2})^{3}\times 5^{4})\div 5^{7}$

can be simplified as

$=[5^{(2\times 3)}\times 5^4]\div 5^7$

$=[5^{6}\times 5^4]\div 5^7$

$=[5^{(6+4)}]\div 5^7$

$=[5^{10}]\div 5^7$

$=5^{10-7}$

$=5^3$

Question: 2(iii) Simplify and express each of the following in exponential form:

$(iii)\: 25^{4}\div 5^{3}$

Answer:

$(iii)\: 25^{4}\div 5^{3}$

can be simplified as

$=(5^2)^4\div 5^3$

$=5^{(2\times 4)}\div 5^3$

$=5^8\div 5^3$

$=5^{(8-3)}$

$=5^{5}$

Question: 2(iv) Simplify and express each of the following in exponential form:

$(iv)\: \frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}}$

Answer:

$(iv)\: \frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}}$

can be simplified as

$= \frac{3\times 7^{2}\times 11^{8}}{3\times 7\times 11^{3}}$

$=3^{(1-1)}\times 7^{(2-1)}\times 11^{(8-3)}$

$=3^{0}\times 7^{1}\times 11^{5}$

$=7^{1}\times 11^{5}$

Question: 2(v) Simplify and express each of the following in exponential form:

$(v)\: \frac{3^{7}}{3^{4}\times 3^{3}}$

Answer:

$(v)\: \frac{3^{7}}{3^{4}\times 3^{3}}$

can be simplified as

$=\frac{3^7}{3^{4+3}}$

$=\frac{3^7}{3^{7}}$

$=3^{(7-7)}$

$=3^0$

$=1$

Question: 2(vi) Simplify and express each of the following in exponential form:

$(vi)\: 2^{0}+3^{0}+4^{0}$

Answer:

$(vi)\: 2^{0}+3^{0}+4^{0}$

can be simplified as

$=1+1+1$

$=3$

Question: 2(vii) Simplify and express each of the following in exponential form:

$(vii)\: 2^{0}\times 3^{0}\times 4^{0}$

Answer:

$(vii)\: 2^{0}\times 3^{0}\times 4^{0}$

can be simplified as

$=1\times 1\times 1=1$

Question: 2(viii) Simplify and express each of the following in exponential form:

$(viii)\: (3^{0}+2^{0})\times 5^0$

Answer:

$(viii)\: (3^{0}+2^{0})\times 5^0$

can be simplified as

$=(1+1)\times 1$

$=2\times 1$

$=2$

Question: 2(ix) Simplify and express each of the following in exponential form:

$(ix)\: \frac{2^{8}\times a^{5}}{4^{3}\times a^{3}}$

Answer:

$(ix)\: \frac{2^{8}\times a^{5}}{4^{3}\times a^{3}}$

can be simplified as

$=\frac{2^{8}\times a^{5}}{(2^2)^{3}\times a^{3}}$

$=\frac{2^{8}\times a^{5}}{2^{6}\times a^{3}}$

$=2^{(8-6)}\times a^{(5-3)}$

$=2^{(2)}\times a^{(2)}$

$=(2a)^2$

Question: 2(x) Simplify and express each of the following in exponential form:

$(x)\: (\frac{a^{5}}{a^{3}})\times a^{8}$

Answer:

$(x)\: (\frac{a^{5}}{a^{3}})\times a^{8}$

can be simplified as

$=a^{(5-3)}\times a^8$

$=a^{(2)}\times a^8$

$=a^{(2+8)}$

$=a^{(10)}$

Question: 2(xi) Simplify and express each of the following in exponential form:

$(xi)\: \frac{4^{5}\times a^{8}b^{3}}{4^{5}\times a^{5}b^{2}}$

Answer:

$(xi)\: \frac{4^{5}\times a^{8}b^{3}}{4^{5}\times a^{5}b^{2}}$

can be simplified as

$=4^{(5-5)}\times a^{(8-5)}\times b^{(3-2)}$

$=4^{0}\times a^{3}\times b^{1}$

$= a^{3}\times b$

Question: 2(xii) Simplify and express each of the following in exponential form:

$(xii)\: (2^{3}\times 2)^{2}$

Answer:

$(xii)\: (2^{3}\times 2)^{2}$

can be simplified as

$=\left(2^{3+1}\right)^2$

$=(2^{(4)})^2$

$=2^{(4 \times 2)}$

$=2^8$

Question: 3 Say true or false and justify your answer:

$(i)\: 10\times 10^{11}=100^{11}$ $(ii)\: 2^{3}> 5^{2}$ $(iii)\: 2^{3}\times 3^{2}= 6^{5}$ $(iv)\: 3^{0}=(1000)^{0}$

Answer:

$(i)\: 10\times 10^{11}=100^{11}$

can be simplified as

$LHS:10^{(1+11)}$

$=10^{(12)}$

Since , $LHS \neq RHS$

Thus, it is false

$(ii)\: 2^{3}> 5^{2}$

can be simplified as

$LHS=2^3=8$

$RHS=5^2=25$

Since, $LHS\ngtr RHS$

Thus, it is false

$(iii)\: 2^{3}\times 3^{2}= 6^{5}$

can be simplified as

$LHS:2^3\times 3^2=8\times 9=72$

$RHS: 6^5=7776$

Since , $LHS \neq RHS$

Thus, it is false

$(iv)\: 3^{0}=(1000)^{0}$

can be simplified as

$LHS: 3^0=1$

$RHS:1000^0=1$

Since, LHS = RHS

Thus, it is true.

Question: 4 Express each of the following as a product of prime factors only in exponential form:

$(i)\: 108\times 192$ $(ii)\: 270$ $(iii)\: 729\times 64$ $(iv)\: 768$

Answer:

$(i)\: 108\times 192$

$108\times 192=(2^2\times 3^3)\times (2^6\times 3)$

$=2^{(2+6)}\times 3^{(3+1)}$

$=2^8\times 3^4$

$(ii)\: 270$

$270=2\times 3^3\times 5$

$(iii)\: 729\times 64$

$729\times 64=3^6\times 2^6$

$(iv)\: 768$

$768=2^8\times 3$

Question: 5(i) Simplify:

$(i)\: \frac{(2^{5})^{2}\times 7^{3}}{8^{3}\times 7}$

Answer:

$(i)\: \frac{(2^{5})^{2}\times 7^{3}}{8^{3}\times 7}$

can be simplified as

$= \frac{2^{(5\times 2)}\times 7^{3}}{(2^3)^{3}\times 7}$

$= \frac{2^{10}\times 7^{3}}{(2^{(3\times 3)})\times 7}$

$= \frac{2^{10}\times 7^{3}}{(2^{9})\times 7}$

$=2^{(10-9)}\times 7^{(3-1)}$

$=2\times 7^{2}$

$=2\times49=98$

Question: 5(ii) Simplify:

$(ii)\frac{25\times 5^{2}\times t^{8}}{10^{3}\times t^{4}}$

Answer:

$(ii)\frac{25\times 5^{2}\times t^{8}}{10^{3}\times t^{4}}$

can be simplified as

$=\frac{5^2\times 5^{2}\times t^{8}}{(2\times 5)^{3}\times t^{4}}$

$=\frac{5^{(2+2)}\times t^{8}}{2^3\times 5^{3}\times t^{4}}$

$=\frac{5^{4}\times t^{8}}{2^3\times 5^{3}\times t^{4}}$

$=\frac{5^{4-3}\times t^{(8-4)}}{2^3}$

$=\frac{5\times t^{4}}{2^3}$

$=\frac{5 t^{4}}{8}$

Question: 5(iii) Simplify:

$(iii)\: \frac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}$

Answer:

$(iii)\: \frac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}$

can be simplified as

$= \frac{3^{5}\times (2\times 5)^{5}\times 5^2}{5^{7}\times (2\times 3)^{5}}$

$= \frac{3^{5}\times 2^5 \times 5^{5}\times 5^2}{5^{7}\times 2^5 \times 3^{5}}$

$= 3^{(5-5)} \times 2^{(5-5)} \times 5^{(5+2-7)}$

$= 3^{0} \times 2^{0} \times 5^{0}$

$= 1 \times 1 \times 1=1$

Question: 1 Write the following numbers in their expanded forms:

279404, 3006194, 2806196, 120719, 20068

Answer:

(i) 279404

$279404=200000+70000+9000+400+00+4$

$=2\times 100000+7\times 10000+9\times 1000+4\times 100+0\times 10+4\times 1$

$=2\times 10^5+7\times 10^4+9\times 10^3+4\times 10^2+0\times 10^1+4\times 10^0$

(ii) 3006194

$3006194=3000000+0+0+6000+100+90+4$

$=3\times 10^6+0\times 10^5+0\times 10^4+6\times 10^3+1\times 10^2+9\times 10^1+4\times 10^0$

(iii) 2806196

$2806196=2000000+800000+0+6000+100+90+6$

$=2\times 1000000+8\times 100000+0\times 10000+6\times 1000+1\times$ $100+9\times 10+6\times 1$

$=2\times 10^6+8\times 10^5+0\times 10^4+6\times 10^3+1\times 10^2+9\times 10^1+6\times 10^0$

(iv) 120719

$120719=100000+20000+0+700+10+9$

$=1\times 100000+2\times 10000+0\times 1000+7\times 100+1\times 10+9\times 1$ $=1\times 10^5+2\times 10^4+0\times 10^3+7\times 10^2+1\times 10^1+9\times 10^0$

(v) 20068

$20068=20000+0+0+60+8$

$=2\times 10000+0\times 1000+0\times 100+6\times 10+8\times 1$

$=2\times 10^4+0\times 10^3+0\times 10^2+6\times 10^1+8\times 10^0$

Question: 2 Find the number from each of the following expanded forms:

$(a)\: 8\times 10^{4}+6\times 10^{3}+0\times 10^{2}+4\times 10^{1}+5\times 10^{0}$

$(b)\: 4\times 10^{5}+5\times 10^{3}+3\times 10^{2}+2\times 10^{0}$

$(c)\: 3\times 10^{4}+7\times 10^{2}+5\times 10^{0}$

$(d)\: 9\times 10^{5}+2\times 10^{2}+3\times 10^{1}$

Answer:

$(a)\: 8\times 10^{4}+6\times 10^{3}+0\times 10^{2}+4\times 10^{1}+5\times 10^{0}$

$=8\times 10000+6\times 1000+0\times 100+4\times 10+5\times 1$

$=80000+6000+000+40+5$

$=86045$

$(b)\: 4\times 10^{5}+5\times 10^{3}+3\times 10^{2}+2\times 10^{0}$

$=4\times 100000+0\times 10000+5\times 1000+3\times 100+0\times 10+2\times 1$

$=400000+00000+5000+300+00+2$

$=405302$

$(c)\: 3\times 10^{4}+7\times 10^{2}+5\times 10^{0}$

$=3\times 10000+0\times 1000+7\times 100+0\times 10+5\times 1$

$=30000+0000+700+00+5$

$=30705$

$(d)\: 9\times 10^{5}+2\times 10^{2}+3\times 10^{1}$

$=9\times 100000+0\times 10000+0\times 1000+2\times 100+3\times 10+0\times 1$

$=900000+00000+0000+200+30+0$

$=900230$

Thus, the above problems are simplified in simpler forms.

Question: 3 Express the following numbers in standard form:

(i) 5,00,00,000 (ii) 70,00,000 (iii) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78

Answer:

(i) 5,00,00,000

$50000000=5\times 10000000=5\times 10^7$

(ii) 70,00,000

$7000000=7\times 1000000=7\times 10^6$

(iii) 3,18,65,00,000

$3186500000=31865\times 100000$

$=3.1865\times 10000 \times 100000$

$=3.1865\times 10^9$

(iv) 3,90,878

$=3.90878\times 100000$

$=3.90878\times 10^5$

(v) 39087.8

$=3.90878\times 10000$

$=3.90878\times 10^4$

(vi) 3908.78

$=3.90878\times 1000$

$=3.90878\times 10^3$

Question: 4 Express the number appearing in the following statements in standard form.

(a) The distance between Earth and the Moon is 384,000,000 m.

(b) The speed of light in a vacuum is 300,000,000 m/s.

(c) The diameter of the Earth is 1,27,56,000 m.

(d) The diameter of the Sun is 1,400,000,000 m.

(e) In a galaxy, there are, on average, 100,000,000,000 stars.

(f) The universe is estimated to be about 12,000,000,000 years old.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

(i) The earth has 1,353,000,000 cubic km of seawater.

(j) The population of India was about 1,027,000,000 in March 2001.

Answer:

(a) The distance between Earth and Moon = 384,000,000 m

$=384\times 1000000$

$=3.84 \times 100\times 1000000$

$=3.84 \times 10^8m$

(b) Speed of light in vacuum =300,000,000 m/s.

$=3\times 100000000$

$=3\times 10^8$

(c) Diameter of the Earth = 1,27,56,000 m.

$=12756\times 1000$

$=1.2756\times 10000\times 1000$

$=1.2756\times 10^7m$

(d) Diameter of the Sun = 1,400,000,000 m.

$=14\times 100000000$

$=14\times 10^8m$

$=1.4\times 10^9m$

(e) In a galaxy, there are on average = 100,000,000,000 stars.

$=1\times 100000000000$

$=1\times 10^{11}$

(f) The universe is estimated to be about 12,000,000,000 years old.

$=1.2\times 10000000000$

$=1.2\times 10^{10}years$

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated = 300,000,000,000,000,000,000 m.

$=3\times 100000000000000000000000000000$

$=3 \times 10^{19}$

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

60,230,000,000,000,000,000,000

$= 6023\times 10000,000,000,000,000,000$

$= 6023\times 10^{19}$

(i) The earth has 1,353,000,000 cubic km of seawater.

$=1.353\times 1000000000$

$=1.353\times 10^9 km^3$

(j) The population of India was about 1,027,000,000 in March 2001.

$=1.027\times 1000000000$

$=1.027\times 10^9$

Exponents and Powers Class 7 Maths Chapter 11- Topics

• Exponents
• Laws Of Exponents
• Multiplying Powers With The Same Base
• Dividing Powers With The Same Base
• Taking Power Of A Power
• Multiplying Powers With The Same Exponents
• Dividing Powers With The Same Exponents
• Miscellaneous Examples Using The Laws Of Exponents
• Decimal Number System
• Expressing Large Numbers In The Standard Form

NCERT Solutions for Class 7 Maths Chapter 11 Exponents and Powers - Points to Remember

For any non-zero integers, a and b and whole numbers m and n, it obeys certain properties given below

• $\ a^m\times a^n=a^{m+n}$
• $\frac{a^m}{a^n}=a^{m-n}$
• $\ (a^m)^n=a^{mn}$
• $a^{m} \times b^{m}=(a b)^{m}$
• $a^{m} \div b^{m}=(\frac{a}{b})^m$
• $a^{0}=1$
• $(-1)^{\text {even number }}=1$
• $(-1)^{\operatorname{odd} \operatorname{number}}=-1$

NCERT Solutions for Class 7 Maths Chapter Wise

NCERT Solutions for Class 7 Subject Wise

Students can refer to the link below to access the subject-wise solutions for Class 7.

• NCERT Solutions for Class 7 Maths
• NCERT Solutions for Class 7 Science

NCERT Books and NCERT Syllabus

• NCERT Syllabus Class 7 Maths
• NCERT Books Class 7
• NCERT Syllabus Class 7