# NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

Written by Team Trustudies
Updated at 2021-05-07

## NCERT solutions for class 7 Maths Chapter 13 Exponents And Powers Exercise 13.1

Q.1 Find the value of
(i) ${2}^{6}$
(ii)${9}^{3}$
(iii) ${11}^{2}$
(iv) ${5}^{4}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) ${2}^{6}=2×2×2×2×2×2=64$
(ii) ${9}^{3}=9×9×9=729$
(iii) ${11}^{2}=11×11=121$
(iv)${5}^{4}=5×5×5×5=625$

Q.2 Exress the following in exponential form:
(i) 6 × 6 × 6 × 6
(ii) t × t
(iii) b × b × b × b
(iv) 5 × 5 × 7 × 7 × 7
(v) 2 × 2 × a × a
(vi) a × a × a × c × c × c× c × d

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) $6×6×6×6={6}^{3}$
(ii)$t×t={t}^{2}$
(iii) $b×b×b×b={b}^{4}$
(iv) $5×5×7×7×7={5}^{2}×{7}^{3}={5}^{2}·{7}^{3}$
(v) $2×2×a×a={2}^{2}×{a}^{2}={2}^{2}·{a}^{2}$
(vi)$a×a×a×c×c×c×c×d={a}^{3}×{c}^{4}×d={a}^{3}·{c}^{4}·d$

Q.3 Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(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= ${5}^{5}$

Q.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) ${2}^{10}or{10}^{2}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) ${4}^{3}or{3}^{4}$
${4}^{3}=4×4×4=64,$
${3}^{4}=3×3×3×3=81$
Since 81 > 64
$?{3}^{4}>{4}^{3}.$
(ii)${5}^{3}or{3}^{5}$
${5}^{3}=5×5×5=125$
${3}^{5}=3×3×3×3×3=243$
Since 243 > 125
${3}^{5}>{5}^{3}.$
(iii)${2}^{8}or{8}^{2}$
${2}^{8}=2×2×2×2×2×2×2×2=256$
${8}^{2}=8×8=64$
Since 256 > 64
${2}^{8}>{8}^{2}.$
(iv) ${100}^{2}or{2}^{100}$ ${100}^{2}=100×100=10000$
${2}^{100}=2×2×2×\dots 100times=214=16384$
Since 16384 > 10,000
${2}^{100}>{100}^{2}.$
(v)${2}^{10}or{10}^{2}$
${2}^{10}=2×2×2×2×2×2×2×2×2×2=1024$
${10}^{2}=10×10=100$
$?{2}^{10}>{10}^{2}.$

Q.5 Express each of the following as the product of powers of their prime
(i) 648
(ii) 405
(iii) 540
(iv) 3600

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) 648= ${2}^{3}×{3}^{4}$
(ii) 405= ${3}^{4}×{5}^{1}$
(iii) $540={2}^{2}×{3}^{3}×{5}^{1}$
(iv) $3600={2}^{4}×{3}^{2}×{5}^{2}$

Q.6 Simplify:
(i) $2×{10}^{3}$
(ii) ${7}^{2}×{2}^{2}$
(iii) ${2}^{3}×5$
(iv) $3×{4}^{4}$
(v) $0×{10}^{2}$
(vi)${5}^{2}×{3}^{3}$
(vii) ${2}^{4}×{3}^{2}$
(viii)${3}^{2}×{10}^{4}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) $2×{10}^{3}=2×10×10×10==2000$
(ii)${7}^{2}×{2}^{2}==7×7×2×2=196$
(iii)${2}^{3}×5=2×2×2×5=40$
(iv) $3×{4}^{4}=3×4×4×4×4=768$
(v)$0×{10}^{2}=0×10×10==0$
(vi) ${5}^{2}×{3}^{3}=5×5×3×3×3=675$
(vii) ${2}^{4}×{3}^{2}=2×2×2×2×3×3=144$
(viii) ${3}^{2}×{10}^{4}=3×3×10×10×10×10=90000$

Q.7 Simplify:
(i)$\left(?4{\right)}^{3}$
(ii)$\left(?3\right)×\left(?2{\right)}^{3}$
(iii)$\left(?3{\right)}^{2}×\left(?5{\right)}^{2}$
(iv)$\left(?2{\right)}^{3}×\left(?10{\right)}^{3}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i)$\left(?4{\right)}^{3}=\left(?4\right)×\left(?4\right)×\left(?4\right)=?64$ [$?$(-a)odd number = (-a)odd number]
(ii) $\left(?3\right)×\left(?2{\right)}^{3}=\left(?3\right)×\left(?2\right)×\left(?2\right)×\left(?2\right)$
$=\left(?3\right)×\left(?8\right)$= 24 [$?$(-a)odd number = (-a)odd number]
(iii)$\left(?3{\right)}^{2}×\left(?5{\right)}^{2}=\left[\left(?3\right)×\left(?5\right){\right]}^{2}$
$={15}^{2}=225\left[?{a}^{m}×{b}^{m}=\left(ab{\right)}^{m}\right]$
(iv)$\left(?2{\right)}^{3}×\left(?10{\right)}^{3}=\left[\left(?2\right)×\left(?10\right){\right]}^{3}$
$={20}^{2}=8000\left[?{a}^{m}×{b}^{m}=\left(ab{\right)}^{m}\right]$

Q.8 Compare the following:
(i)$2.7×{10}^{12};1.5×{10}^{8}$
(ii) $4×{10}^{14};3×{10}^{1}7$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) $2.7×{10}^{12}=2.7×{10}^{4}×{10}^{8}=27000×{10}^{8}$
$27000×{10}^{8}>1.5×{10}^{8}$
$2.7×{10}^{12}>1.5×{10}^{8}$
(ii) $3×{10}^{17}=3×{10}^{3}×{10}^{14}=3000×{10}^{14}$
$3000×{10}^{14}>4×{10}^{14}$
$4×{10}^{14}<3×{10}^{17}$

## NCERT solutions for class 7 Maths Chapter 13 Exponents And Powers Exercise 13.2

Q.1 Using laws of e×ponents, simplify and write the answer in e×ponential form:
(i) ${3}^{2}×{3}^{4}×{3}^{8}$
(ii)${6}^{15}÷{6}^{10}$
(iii)${a}^{3}×{a}^{2}$
(iv)${7}^{x}×{7}^{2}$
(v)$\left({5}^{2}{\right)}^{3}÷{5}^{3}$
(vi) ${2}^{5}×{5}^{5}$
(vii) ${a}^{4}×{b}^{4}$
(viii)$\left({3}^{4}{\right)}^{3}$
(ix)$\left({2}^{20}÷{2}^{15}\right)×{2}^{3}$
(x)${8}^{t}÷{8}^{2}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) ${3}^{2}×{3}^{4}×{3}^{8}={3}^{2+4+8}={3}^{14}\left[{a}^{m}÷{a}^{n}={a}^{m+n}\right]$
(ii) ${6}^{15}÷{6}^{10}={6}^{15?10}={6}^{5}\left[{a}^{m}÷{a}^{n}={a}^{m?n}\right]$
(iii) ${a}^{3}×{a}^{2}={a}^{3+2}={a}^{5}\left[{a}^{m}×{a}^{n}={a}^{m+n}\right]$
(iv)${7}^{x}×{7}^{2}={7}^{x+2}\left[{a}^{m}×{a}^{n}={a}^{m+n}\right]$
(v)$\left({5}^{2}{\right)}^{3}÷{5}^{3}={5}^{2×3}÷{5}^{3}={5}^{6}÷{5}^{3}={5}^{6?3}$
$={5}^{3}\left[\left({a}^{m}{\right)}^{n}={a}^{mn},{a}^{m}÷{a}^{n}={a}^{m?n}\right]$
(vi) ${2}^{5}×{5}^{5}=\left(2×5{\right)}^{5}={10}^{5}\left[{a}^{m}×{b}^{m}=\left(ab{\right)}^{m}\right]$
(vii) ${a}^{4}×{b}^{4}=\left(ab{\right)}^{4}\left[{a}^{m}×{b}^{m}=\left(ab{\right)}^{4}\right]$
(ix)$\left({2}^{20}÷{2}^{15}\right)×{2}^{3}={2}^{20?15}×{2}^{3}={2}^{5}×{2}^{3}={2}^{5+3}={2}^{8}$
(x) ${8}^{t}÷{8}^{2}={8}^{t?2}$

Q.2 Simplify and express each of the following in exponential form:
(i) $\frac{\left({2}^{3}×{3}^{4}×4\right)}{\left(3×32\right)}$
(ii) $\left[\left({5}^{2}{\right)}^{3}×{5}^{4}\right]÷{5}^{7}$
(iii) ${25}^{4}÷{5}^{3}$
(iv) $\frac{3×{7}^{2}×{11}^{8}}{21×{11}^{3}}$
(v) $\frac{{3}^{7}}{{3}^{4}×{3}^{3}}$
(vi) ${2}^{0}+{3}^{0}+{4}^{0}$
(vii) ${2}^{0}×{3}^{0}×{4}^{0}$
(viii) $\left({3}^{0}+{2}^{0}\right)×{5}^{0}$
(ix)$\frac{{2}^{8}×{a}^{5}}{{4}^{3}×{a}^{3}}$
(x) $\left(\frac{{a}^{5}}{{a}^{3}}\right)×{a}^{8}$
(xi) $\frac{{4}^{5}×{a}^{8}{b}^{3}}{{4}^{5}×{a}^{5}{b}^{2}}$
(xii) $\left({2}^{3}×2{\right)}^{2}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) $\frac{{2}^{3}×{3}^{4}×4}{3×32}$ = $\frac{{2}^{3}×{3}^{4}×{2}^{2}}{3×{2}^{5}}$
= $\frac{{2}^{3+2}×{3}^{4}}{3×{2}^{5}}$=$\frac{{2}^{5}×{3}^{4}}{3×{2}^{5}}$
= ${2}^{5?5}×{3}^{4?1}$ = ${2}^{0}×{3}^{3}$= ${3}^{3}$
(ii)$\left[\left({5}^{2}{\right)}^{3}×{5}^{4}\right]÷{5}^{7}$ = $\left({5}^{6}×{5}^{4}\right)÷{5}^{7}$
= $\left({5}^{6+4}÷{5}^{7}$ = ${5}^{10?7}$ = ${5}^{3}$
(iii) ${25}^{4}÷{5}^{3}$ = $\left({5}^{2}{\right)}^{4}÷{5}^{3}$= ${5}^{8}÷{5}^{3}$ = ${5}^{8?3}$= ${5}^{5}$
(iv) $\frac{3×{7}^{2}×{11}^{8}}{21×{11}^{3}}$ = $\frac{3×{7}^{2}×{11}^{8}}{7×3×{11}^{3}}$
= ${7}^{2?1}×{11}^{8?3}$ = $7×{11}^{5}$ \) (v) $\frac{{3}^{7}}{{3}^{4}×{3}^{3}}$ = $\frac{{3}^{7}}{{3}^{4+3}}$ = $\frac{{3}^{7}}{{3}^{7}}$ = 1
(vi) ${2}^{0}+{3}^{0}+{4}^{0}$ = 1+1+1 = 0$\left[?{a}^{0}=1\right]$
(vii) ${2}^{0}×{3}^{0}×{4}^{0}$ = 1×1×1 = 1
(viii) $\left({3}^{0}+{2}^{0}\right)×{5}^{0}$ = (1+1)×1=2×1=2
(ix) $\frac{{2}^{8}×{a}^{5}}{{4}^{3}×{a}^{3}}$ = $\frac{{2}^{8}×{a}^{5}}{\left({2}^{2}{\right)}^{3}×{a}^{3}}$
= $\frac{{2}^{8}×{a}^{5}}{{2}^{6}×{a}^{3}}$ = $$2^{8-6}{×a^{5-3}$$ = ${2}^{2}×{a}^{2}$ = $\left(2a{\right)}^{2}$
(x) $\left(\frac{{a}^{5}}{{a}^{3}}\right)×{a}^{8}$ = $\frac{{a}^{5+8}}{{a}^{3}}$ = $\frac{{a}^{13}}{{a}^{3}}$
= ${a}^{13?3}$ = ${a}^{10}$
(xi) $\frac{{4}^{5}×{a}^{8}{b}^{3}}{{4}^{5}×{a}^{5}{b}^{2}}$ = $\frac{{a}^{8}{b}^{3}}{{a}^{5}{b}^{2}}$
= ${a}^{8?5}{b}^{3?2}$ = ${a}^{3}b$
(xii) $\left({2}^{3}×2{\right)}^{2}$ = ${2}^{6}×{2}^{2}$ = ${2}^{6+2}$ = ${2}^{8}$

Q.3 Say true or false and justify your answer: (i)$10×{10}^{1}1={100}^{1}1$
(ii) ${2}^{3}>{5}^{2}$
(iii)${2}^{3}×{3}^{2}={6}^{5}$
(iv) ${3}^{2}0=\left(1000{\right)}^{0}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i)LHS = $10×{10}^{1}1={10}^{1+11}={10}^{12}$
RHS$={100}^{1}1=\left({10}^{2}{\right)}^{1}1={10}^{2}2$
${10}^{1}2?{10}^{2}2$
$?$ Statement is false.
(ii)${2}^{3}>{5}^{2}$
LHS = ${2}^{3}=8$
RHS =${5}^{2}=25$
8 < 25
$?{2}^{3}<{5}^{2}$
Thus, the statement is false.
(iii) ${2}^{3}×{3}^{2}={6}^{5}$
LHS $={2}^{3}×{3}^{2}=8×9=72$
RHS $={6}^{5}=6×6×6×6×6=7776$
$72?7776$
$?$The statement is false.
(iv)${3}^{0}=\left(1000{\right)}^{0}$
LHS = ${3}^{0}=1$
RHS = $\left(1000{\right)}^{0}=1$
LHS = RHS

Q.4 Express each of the following as a product of prime factors only in exponential form:
(i) 108 × 192
(ii) 270
(iii) 729 × 64
(iv) 768

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) 108 × 192 = 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
=${2}^{8}×{3}^{4}$
(ii) $270=2×3×3×3×5=2×{3}^{3}×5$
(iii) 729 × 64 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2
$={3}^{6}×{2}^{6}$
(iv) 768 = 2×2×2×2×2×2×2×2×3 = ${2}^{8}×3$

Q.5 Simplify:
(i) $\frac{\left({2}^{5}{\right)}^{2}×{7}^{3}}{{8}^{3}×7}$
(ii) $\frac{25×{5}^{2}×{t}^{8}}{{10}^{3}×{t}^{4}}$
(iii) $\frac{{3}^{5}×{10}^{5}×25}{{5}^{7}×{6}^{5}}$

NCERT Solutions for Class 7 Maths Chapter 13 Exponents And Powers

(i) $\frac{\left({2}^{5}{\right)}^{2}×{7}^{3}}{{8}^{3}×7}$ = $\frac{\left({2}^{10}×{7}^{3}}{\left({2}^{3}{\right)}^{3}×7}$
= $$\frac{(2^{10}× 7^3}{{2^9 × 7}$$ = ${2}^{10?9}×{7}^{3?1}$ = ${2}^{1}×{7}^{2}$ =2× 49 = 98
(ii) $\frac{25×{5}^{2}×{t}^{8}}{{10}^{3}×{t}^{4}}$ = $\frac{{5}^{2}×{5}^{2}×{t}^{8}}{{2}^{3}×{5}^{3}×{t}^{4}}$
= $\frac{{5}^{4}×{t}^{8}}{{2}^{3}×{5}^{3}×{t}^{4}}$ = $\frac{{5}^{4?3}×{t}^{8?4}}{{2}^{3}}$ = $\frac{5{t}^{4}}{{2}^{3}}$
(iii) $\frac{{3}^{5}×{10}^{5}×25}{{5}^{7}×{6}^{5}}$= $\frac{{3}^{5}×{2}^{5}×{5}^{5}×{5}^{2}}{{5}^{7}×{2}^{5}×{3}^{5}}$