# 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 $10^2$

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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, $2^{10}$>$10^2$

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