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 $10^2$

AcademicMathematicsNCERTClass 7

Given: 

$(i)$. $4^{3}$ 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 $10^2$


To do: To identify the greater number, wherever possible, in each of the cases.


Solution: 
$(i)$. $4^3$ or $3^4$


$4^3=4\times4\times4$


$=64$


Now, $3^4=3\times3\times3\times3$


$=81$


Since, $64$<$81$


Thus, $3^4$ is greater than $4^3$


$(ii)$. $5^3$ or $3^5$


$5^3=5\times5\times5$


$=125$


$3^5=3\times3\times3\times3\times3$


$=243$


Since, $125$<$243$


$(iii)$. $2^8$ or $8^2$

$2^8=2\times2\times2\times2\times2\times2\times2\times2$

$=256$

$8^2=8\times8$


$=64$


Since, $256$>$64$


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


$(iv)$. $100^2$ or $2^{100}$


$100^2$


$=100\times100$


$=10,000$


$2^{100}=2\times2\times2\times2\times2.......95\ times.... $


$=2000.......$


$2^{100}$ is greater than $100^2$


$(v)$. $2^{10}$ or $10^2$


$2^{10}=2\times2\times2\times2\times2\times2\times2\times2\times2\times2$


$=1024$


And $10^2=10\times10$


$=100$


On comparing,


$1024$>$100$


So, $2^{10}$>$10^2$

raja
Updated on 10-Oct-2022 13:38:51

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