Question

Find the last digit of 2^1999 x 2^2013.

Answer 1

Answer:

math error

Step-by-step explanation:

so it cannot be solved rightly

Answer 2

Answer:

6

Step-by-step explanation:

Step 1.

let's take powers of 2 till last digit repeat

We are taking the last digit only

2¹ = 2 Step 1

2²= 4 Step 2

2³= 8 Step 3

2⁴= 6 Step 4

2⁵= 2 ( here the last digit repetition started so, we will take till power 4.

Step 2.

The 1 cycle contains four steps above. Now, we have to find how much cycle and steps it's take in our question so that we can decide the last digit.

2¹⁹⁹⁹ X 2²⁰¹³

The power are 1999 and 2013

Now if we divide the power 1999 and 2013 by 4 (2's one cycle contain 4 steps).

1. In 1999 we get 499 cycle and remainder 3( the remainder is taken as steps). So total of 499 complete cycles and 3 steps.

And the 3rd step contains 8 as the last digit.

the last digit of 2¹⁹⁹⁹ is 8

2. In 2013 we get 503 cycles and remainder 1( the remainder is taken as steps). So total 503complete cycle and 1 step.

And the 1st step contains 2 as the last digit.

the last  digit of 2²⁰¹³ is 2

Step 3.

Now as per question if we multiply the last digit of 2¹⁹⁹⁹  and 2²⁰¹³

8 x 2 = 16

we get a number whose last digit will be 6.