+0

what is the ones digit of 9^40?

0
260
2

what is the ones digit of 9^40?

Guest Feb 23, 2015

Best Answer

#2
+18829
+10

what is the ones digit of 9^40 ?

$$9^{40}\mod 10\\ =( \underbrace{9^2}_{=1\mod 10} )^{20}\mod 10 \qquad | \qquad 9^2\mod 10 =\ 81 \mod 10 =\ 1 \\\\ =1^{20}\mod 10 \qquad\qquad | \quad 1^{20} = 1 \\ =1\mod 10$$

heureka  Feb 24, 2015
Sort:

2+0 Answers

#1
+81023
+10

Note the cycle

9^1 = 9

9^2 = 81

9^3 = 729

9^4 =  6561     and this pattern repeats for every "block" of 4 powers

Note that 40 is evenly divisible by 4, so 9^40 has a "ones" digit that completes this cycle. So....9^40  ends in a "1"

CPhill  Feb 23, 2015
#2
+18829
+10
Best Answer

what is the ones digit of 9^40 ?

$$9^{40}\mod 10\\ =( \underbrace{9^2}_{=1\mod 10} )^{20}\mod 10 \qquad | \qquad 9^2\mod 10 =\ 81 \mod 10 =\ 1 \\\\ =1^{20}\mod 10 \qquad\qquad | \quad 1^{20} = 1 \\ =1\mod 10$$

heureka  Feb 24, 2015

11 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details