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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 $10^2$
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, $2^{10}$>$10^2$