What is the units digit of 99^99 × 44^44 × 66^66?

Question

What is the units digit of  99^{99} × 44^{44} × 66^{66} ?

A. 0 
B. 2 
C. 4 
D. 6 
E. 8

chetan2u · Answer

since we are looking for units digit, we require to be concerned with ONLY units digit of three terms..
 1) 9 gives 9 as units digit if to the power of ODD and 1 if to the power of EVEN.. 
here it is ODD, so units digit = 9
 2) 4 gives 4 as units digit if to the power of ODD and 6 if to the power of EVEN.. 
here it is EVEN, so units digit = 6
 3) 6 gives 6 as units digit irrespective of any POSITIVE integer as power 
so here units digit = 6..

therefore UNITS digit of entire term will be same as that of 9*6*6 = 36*9..
so units digit = 4, as 9*6=54 
C

mathiaskeul · Answer

Units digits of 9

9^2=1 9^3=9 9^4=1 Etc...

9 to an even power gives 1... 
9 to an odd power gives 9...

Units digits of 4 
4^2= 6 4^3=4 4^4=6 Etc...

4 to an even power gives 6... 
4 to an odd power gives 4...

Units digit of 6 
ALWAYS 6

9*6*6 = 324 so digit number of 4 answer C

Abhishek009 · Answer

9^{odd} = Units digit 9

4^{odd} = Units digit 6

6^{odd/even} = Units digit 6

So we have here ,  99^{99} × 44^{44} × 66^{66}  => 9 x 6 x 6 =>5  4  x  6    =>   6 x 4   = 2  4

Hence last digit will be 4

Abhishek009 · Answer

99^{99}  will have units digit as 9
 44^{44}  will have units digit as 6
 66^{66}  will have units digit as 6

So, the units digit will be  9*6*6 = 54*6 = x4

Thus, the correct answer must be (C) 4

Mkrishnabdrr · Answer

9^{odd} * 4^{even} * 6^{66}  (0,1,5,6 has the same last digit as the base, 9 and 4 both have the cyclicity of 2, when 9 or 4 is odd same as base, when 9 is even last digit = 1, when 4 is even last digit=6)
=9 x 6 x 6
=54 x 6
=32 4 
Ans is C

RaguramanS · Answer

The unit digit of an equation can be easily found using cyclicity

The equation can be rephrased as

9^99*4^44*6^66*11*209

The unit digit of 9: 9(power odd),1 (Power even)
The unit digit of 4: 4(power odd), 6 (Power Even) 
The unit digit of 6: 6(power Odd, Even)
The unit digit of 11: 1(power Odd, Even)

9*6*6*1= 4(Unit digit)

Option C

JeffTargetTestPrep · Answer

Since we only care about the units digit, we really are trying to determine the units digit of:
 
9^99 x 4^44 x 6^6
 
Let’s first determine the units digit of the base of 9:
 
9^1 = 9
 
9^2 = 1
 
9^3 = 9
 
9^4 = 1
 
We see that 9 raised to an odd exponent produces a units digit of 9, and 9 raised to an even exponent produces a units digit of 1. Thus, 9^99 has a units digit of 9. Next let’s determine the units digit of 4^44.
 
4^1 = 4
 
4^2 = 6
 
4^3 = 4
 
4^4 = 6
 
We see that 4 raised to an odd exponent produces a units digit of 4, and 4 raised to an even exponent produces a units digit of 6. Thus, 4^44 has a units digit of 6. Next, let’s determine the units digit of 6^66.
 
6^1 = 6
 
6^2 = 6
 
6^3 = 6
 
We see that 6 raised to any whole number exponent produces a units digit of 6.
 
Thus, the units digit of 9^99 x 4^44 x 6^6 = 9 x 6 x 6 = 9 x 36; since the units digit of 9 x 36 is equal to the units digit of 9 x 6 = 54, the product has a units digit of 4.
 
Answer: C

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What is the units digit of 99^99 × 44^44 × 66^66?

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What is the units digit of 99^99 × 44^44 × 66^66?

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