Exercise 11.1 (Revised) - Chapter 13 - Exponents & Powers - Ncert Solutions class 7 - Maths
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Chapter 11 - Exponents & Powers - NCERT Solutions Class 7 Maths
Ex 11.1 Question 1.
Find the value of:
(i) $2^6$
(ii) $9^3$
(iii) $11^2$
(iv) $5^4$
Answer:
(i) $2^6=2 \times 2 \times 2 \times 2 \times 2 \times 2=64$
(ii) $9^3=9 \times 9 \times 9=729$
(iii) $11^2=11 \times 11=121$
(iv) $5^4=5 \times 5 \times 5 \times 5=625$
Ex 11.1 Question 2.
Express the following in exponential form:
(i) $6 \times 6 \times 6 \times 6$
(ii) $\mathrm{txt}$
(iii) $\mathrm{b} \times \mathrm{b} \times \mathrm{b} \times \mathrm{b}$
$\begin{array}{ll}\text { (iv) } 5 \times 5 \times 7 \times 7 \times 7 & \text { (v) } 2 \times 2 \times \text { a x a }\end{array}$
(vi) axaxaxcxcxcxcxd
Answer:
(i) $6 \times 6 \times 6 \times 6=6^4$
(ii) $t x t=t^2$
(iii) $\mathrm{b} \times \mathrm{b} \times \mathrm{b} \times \mathrm{b}=\mathrm{b}^4$
(iv) $5 \times 5 \times 7 \times 7 \times 7=5^2 \times 7^3$
(v) $2 \times 2 \times a \times a=2^2 \times a^2$
(vi) axaxaxcxcxcxcxd $=\mathrm{a}^3 \mathrm{xc}^4 \mathrm{xd}$
Ex 11.1 Question 3.
Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125
Answer:
(i) $512=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2=2^9$
(ii) $343=7 \times 7 \times 7=7^3$
(iii) $729=3 \times 3 \times 3 \times 3 \times 3 \times 3=3^6$
(iv) $3125=5 \times 5 \times 5 \times 5 \times 5=5^5$
Ex 11.1 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) $4^3=4 \times 4 \times 4=64$
$
3^4=3 \times 3 \times 3 \times 3=81
$
Since $64<81$
Thus, $3^4$ is greater than $4^3$.
(ii) $5^3=5 \times 5 \times 5=125$
$
3^5=3 \times 3 \times 3 \times 3 \times 3=243
$
Since, $125<243$
Thus, $3^4$ is greater than $5^3$.
(iii) $2^8=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2=256$
$
8^2=8 \times 8=64
$
Since, $256>64$
Thus, $2^8$ is greater than $8^2$.
(iv) $100^2=100 \times 100=10,000$
$
2^{100}=2 \text { x } 2 \text { x } 2 \text { x } 2 \text { x } 2 \text { x ..... } 14 \text { times x ......... x } 2=16,384 \text { x ..... x } 2
$
Since, $10,000<16,384$ x ....... X 2
Thus, $2^{100}$ is greater than $100^2$.
(v) $2^{10}=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2=1,024$
$
10^2=10 \times 10=100
$
Since, $1,024>100$
Thus, $2^{10}>10^2$
Ex 11.1 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) $648=2^3 \times 3^4$
(ii) $405=5 \times 3^4$
(iii) $540=2^2 \times 3^3 \times 5$
(iv) $3,600=2^4 \times 3^2 \times 5^2$
Ex 11.1 Question 6.
Simplify:
(i) $2 \times 10^3$
(ii) $7^2 \times 2^2$
(iii) $2^3 \times 5$
(iv) $3 \times 4^4$
(v) $0 \times 10^2$
(vi) $5^2 \times 3^3$
(vii) $2^4 \times 63^2$
(viii) $3^2 \times 10^4$
Answer:
(i) $2 \times 10^3=2 \times 10 \times 10 \times 10=2,000$
(ii) $7^2 \times 2^2=7 \times 7 \times 2 \times 2=196$
(iii) $2^3 \times 5=2 \times 2 \times 2 \times 5=40$
(iv) $3 \times 4^4=3 \times 4 \times 4 \times 4 \times 4=768$
(v) $0 \times 10^2=0 \times 10 \times 10=0$
(vi) $5^2 \times 3^3=5 \times 5 \times 3 \times 3 \times 3=675$
(vii) $2^4 \times 63^2=2 \times 2 \times 2 \times 2 \times 3 \times 3=144$
(viii) $3^2 \times 10^4=3 \times 3 \times 10 \times 10 \times 10 \times 10=90,000$
Ex 11.1 Question 7.
Simplify:
(i) $(-4)^3$
(ii) $(-3) \times(-2)^3$
(iii) $(-3)^2 \times(-5)^2$
(iv) $(-2)^3 \times(-10)^3$
Answer:
(i) $(-4)^3=(-4) \times(-4) \times(-4)=-64$
(ii) $(-3) \times(-2)^3=(-3) \times(-2) \times(-2) \times(-2)=24$
(iii) $(-3)^2 \times(-5)^2=(-3) \times(-3) \times(-5) \times(-5)=225$
(iv) $(-2)^3 \times(-10)^3=(-2) \times(-2) \times(-2) \times(-10) \times(-10) \times(-10)=8000$
Ex 11.1 Question 8.
Compare the following numbers:
(i) $2.7 \times 10^{12} ; 1.5 x 10^8$
(ii) $4 \times 10^{14} ; 3 \times 10^{17}$
Answer:
(i) $2.7 \times 10^{12}$ and $1.5 x 10^8$
On comparing the exponents of base 10 ,
$
2.7 \times 10^{12}>1.5 x 10^8
$
(ii) $4 \times 10^{14}$ and $3 \times 10^{17}$
On comparing the exponents of base 10 ,
$
4 \times 10^{14}<3 \times 10^{17}
$
