Question

Find the unit digit of the following exponential numbers.

a)   (24)5       b)  (82)10​

Answer 1

Answer:

(24)5 = 24x24x24x24x24

Here base is 24 and unit digit is 4.  We have to first find the cyclicity,  The cyclicity table of 4 is 2.

We know the cyclicity of 4 is 2

Have a look:

4^1 =4

4^2 =16

4^3 =64

4^4 =256

From above it is clear that the cyclicity of 4 is 2.  Now with the cyclicity number i.e. with 2, let us divide the given power i.e. 5 by 2,  the remainder will be 1 so the answer when 4 raised to the power one is 4.So the unit digit, in this case, is 4.

b)  (82)10​

Cyclicity of 2 is 4. The cyclicity chart of 2 is:

2^1 =2

2^2 =4

2^3 =8

2^4=16

2^5=32

Let us divide the given power i.e ten by 2.  the remainder will be 0.   If the remainder becomes zero in any case then the unit digit will be the last digit of  acyclicity number. that is 2.

Step-by-step explanation:

Unit digit of a number is the digit in the one,s place of the number.Cyclicity of any number is about the last digit and how they appear in a certain defined manner.

Hope it helps

Answer 2

$\mathsf\red{{24}^{5}}$

We have to find the unit digit

$\mathsf\red{trick \: :}$

• For number 4 If the power is even then unit digit is 6
• For number 4 if the power is odd then unit digit is 4

so $\mathsf{{24}^{5}}$

power is odd --- so unit digit is 4

_______________________________

$\mathsf\red{{82}^{10}}$

We have to find the unit digit

$\mathsf\red{trick \: :}$

• For number 2 If the power is even then unit digit is 4,6
• For number 2 if the power is odd then unit digit is 2,8

so $\mathsf{{82}^{10}}$

power is even --- so unit digit is 4

$\mathsf{}$

${\tt{\fcolorbox{black}{pink}{© \: ITZBFF}}}$