Question Number 8357 by Nayon last updated on 09/Oct/16
$${who}\:{is}\:{bigger}\:? \\ $$$$\mathrm{1000}^{\mathrm{1000}} \:{or}\:\mathrm{101}^{\mathrm{999}\:} \\ $$$${please}\:{answer}\:{in}\:{details}. \\ $$$$ \\ $$
Commented by Rasheed Soomro last updated on 09/Oct/16
![As 1000>101 ∧ 1000>999 1000^(1000) >101^(999) [∵a>b & x>y⇒a^x >b^y ]](Q8365.png)
$$\mathrm{As}\:\:\:\:\:\mathrm{1000}>\mathrm{101}\:\:\wedge\:\:\mathrm{1000}>\mathrm{999} \\ $$$$\:\:\:\:\:\:\mathrm{1000}^{\mathrm{1000}} >\mathrm{101}^{\mathrm{999}} \:\:\:\left[\because\mathrm{a}>\mathrm{b}\:\&\:\mathrm{x}>\mathrm{y}\Rightarrow\mathrm{a}^{\mathrm{x}} >\mathrm{b}^{\mathrm{y}} \:\right] \\ $$