Say true or false and justify your answer:
$(i)$. $10\times10^{11}=100^{11}$
$(ii)$. $2^3$>$5^2$
$(iii)$. $2^3\times3^2=6^5$
$(iv)$. $3^0=(1000)^0$

Given: 

$(i)$. $10\times10^{11}=100^{11}$

$(ii)$. $2^3$>$5^2$

$(iii)$. $2^3\times3^2=6^5$

$(iv)$. $3^0=(1000)^0$


To do: To state true or false and justify the answer.

Solution:

 $(i)$. $10\times10^{11}=100^{11}$
 
LHS $=(10^{1+11})$                                          $a^m\times a^n=a^{m+n}$

$=10^{12}$
RHS $==(10^2)^11$

$= (10)^{2\times11}$

$= 10^{22}$

Thus the above equation is false.

$(ii)$. $2^3>5^2$

Or $2\times2\times2$>$5\times5$

Or $8>25$

But 8<25

Thus the above equation is false.

$(iii)$. $2^3\times3^2=6^5$

Or
LHS $=2\times2\times2\times3\times3$
$=9\times8$
$=72$

RHS $=6\times6\times6\times6\times6\times=7776$

But $LHS≠RHS$

Thus the above equation is false.

$(iv)$. $3^0=(1000)^0$

$1=1$                                                    $[\because a^0=1]$

$LHS=RHS$

Thus the equation is true.

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Updated on: 10-Oct-2022

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