Find the sum of the last ten digits: 5^(23) ∙ 2^(2022) − 2023


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Question Number 184877 by Shrinava last updated on 13/Jan/23

$Find the sum of the last ten digits :$ $5^{23} \cdot 2^{2022} - 2023$
	Answered by Rasheed.Sindhi last updated on 14/Jan/23

	$5^{23} \cdot 2^{2022} - 2023$ $5^{23} \cdot 2^{23} \cdot 2^{1999} - 2023$ $2^{1999} . 10^{23} - 2023$ $2^{1999} \cdot 1 \underset{23 z e r o s}{\underset{⏟}{00000 . . . 0000}} - 2023$ $= . . . a \underset{23 z e r o e s}{\underset{⏟}{000 . . . 00}} - 2023$ $a, t h e 24 t h d i g i t f r o m r i g h t, i s a$ $n o n - z e r o d i g i t$ $W e n e e d b o r r o w i n o r d e r t o s u b t r a c t 2023$ $A f t e r b o r r o w i n g :$ $L a s t 24 d i g i t s w i l l b e c h a n g e d :$ $\overset{―}{(a - 1) \underset{⏟}{99999 . . . 9 9 9} (10)}$ $\underline{- 2 0 2 3}$ $\underset{L a s t 23 n u m b e r s}{\underset{⏟}{9 9 9 . . . 9 9 9 7 9 7 7}}$ $L a s t t e n d i g i t s : 9999997977$
	Commented by Shrinava last updated on 15/Jan/23

	$thank you dear professor cool$
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