There's A Simple Way To Find The Units Digit Of This Number

7^4 has unit digit 1 as 7^3 has unit digit 3 and then 7 is multiplied to it. Now 7^5 has unit digit 7. So, 7*1=7

7^1 =7 7^2=49 7^3=343 7^4=2401 7^5=16807 ......

we just have to see the unit digit.

so the unit digit is repeating itself after 4 tims. so it's cyclicity is 4.

now in 117^4 = ?????????? whatever it is .. we just have to see the unit digit of 117 which is 7 and it's power which is 4.

and previously i showed you that 7^4 results in 1 at the unit's place ..

and in 347^5 should be dealt in he same manner

7^5 results in 7 at the unit place.

so overall the unit digit of 117^4 X 347^5 = unit digit of 7^4 X unit digit of 7^5 = 1X7 = 7 = answer

Unit digit of a product is equal to the product of the unit digits of each factor, so we want the unit digit of $7^4\cdot 7^5=7^9$ , which is 7.

The remainder upon division of $117^4 \cdot 347^5$ by 10 is the units digit of $117^4 \cdot 347^5$ . $117^4 \cdot 347^5 \equiv 7^9 \equiv 7(49)^4 \equiv 7(81)^2 \equiv 7 \mod 10$ .

To solve this problem, only pay attention to the units digits because we are only trying to find the units digit. of the final product.

Therefore, we have to calculate the units digit of $7^{4} \times 7^{5}$ . Since the units digits of seven have a pattern

* 7, 9, 3, 1, 7, 9... *

We can see that the units digit of $7^{4}$ is 1, and for $7^{5}$ it is 7.

Now what is left is to calculate $7 \times 1$ , which is $\boxed{7}$ , our answer

here we have to find only unit digit so we can solve that only by using unit digit like 7^4=> 7x7x7x7=> 2401 and 7^5=> 7x7x7x7x7=> 16807 again we have to multiply only unit digit thus, 7x1=> 7 that's answer

Let's take the units digit of both bases, which is 7. We see hat the act of repeatedly multiplying 7 by itself produces a pattern in the units digits of the results, starting with the digit 7: 7x7=49 49x7=343 343x7=2401 2401x7=16807 16807x7=117649 and so on. So, we can conclude that there is a pattern cycling between 7, 9, 3, and 1 repeatedly.

since 117 is being raised to the fourth power, the units digit must be the fourth digit in the sequence, which is 1. since 347 is being raised to the power of 5, the sequence would cycle back to the first term after reaching the fourth-7 since the units digits are multiplied by each other during multiplication, 1x7=7. the answer is 7.

7 is the only possible unit

$117 \equiv 7 \pmod{10}$ $\Rightarrow$ $117^4 \equiv 7^4 \pmod{10}$ $\rightarrow$ 1

Since we know,

$7^4 \equiv 1 \pmod{10}$ $\rightarrow$ 2

From 1 & 2, we get

$117^4 \equiv 1 \pmod{10}$ $\rightarrow$ 3

$347 \equiv 7 \pmod{10}$ $\Rightarrow$ $347^5 \equiv 7^5 \pmod{10}$ $\rightarrow$ 4

Since we know,

$7^5 \equiv 7 \pmod{10}$ $\rightarrow$ 5

From 4 & 5, we get

$347^5 \equiv 7 \pmod{10}$ $\rightarrow$ 6

Multipling 6 & 3

$117^4 \times 347^5 \equiv 7 \pmod{10}$

Hence, units digit of $117^4 \times 347^5$ is 7.

its seven

7^4 gives unit digit 1, so we see in problem 7^5 gives unit digit 7. multiply these two 1*7 gives unit digit 7.

the unit digit of 7^4 is 1 and the unit digit of 7^5 is 7, hence the unit digit for 7^4 x 7^5 is 1 x 7 = 7

unit digit of : 7^1=7 , 7^2=9 ; 7^3=3 , 7^4=1 , 7^5=7 , ................................. the patern repeats. Now 7^4 has unit digit 1 & 7^5 has unit digit 7 therefore 1x 7=7 hence unit digit of the question is 7

The answer is 7

7^4 unit digit is 1 and 7^4* 7^4 * 7 unit digit =1 * 1 * 7= 7. (Since 7^5=7^4 * 7)

7^4 unit digit =1, 7^5 unit digit =7, hence 1*7 = 7 result unit digit.

7

7^4 = (7x7) x (7x7) = 49 x 49 = 9 x 9 = 81 = 1 When using modelo 10. 7^5 = 1 x 7 = 7 So the solution ends with 7.

Consider only the units digit. When the units digit is a 7 and is repeatedly multiplied by 7, the units digit of the result follows the following repeating pattern 1,7,9,3,1,7,9,3,... corresponding to (7)^0, (7)^1, (7)^2, (7)^3, (7)^4, (7)^5, (7)^6, (7)^7,.... respectively. Hence (7)^4 of (117)^4 will have the units digit as 1. Similarly (7)^5 of (347)^5 will have units digit as 7. 1x7=7, the solution.

Forget everything; concentrate on units place. 7^4=49 49=whatever that is, 1 on units place. 7^5=49 343=whatever, 7 on units place. 7*1=7 on unit's place of final answer.

7^4=2401 7^5=16807 1*7=7

117 , unit digit is 7 and and 7^4 gives unit digit as 1 , similarly for 347^5 unit digit is again 7 and 7^5 gives unit digit as 7 when unit digit of both these numbers gets multiplied gives the unit digit of product as 1*7 = 7

7^4, the unit is 1, and 7^5 is 7. so, 1 x 7 =7

The units digit of 117^4 is same as the units digit of 7^4. Now, 7^2 = 49 . So, the units digit of 7^4 is same as the units digit of 9*9, which is 1. So, the units digit of 117^4 is 1.

By similar logic, the units digit of 347^5 is same as the units digit of 7^5 = (7^4) * 7, which is 1*7 = 7.

So, the units digit of 117^4 * 347^5 is 1*7 = 7.

last digit in 7^4 is 1 same way 7^5 we can write as 7^4*7=7.So final solution is=7

the question just need the units digits, so we just need to power and multiply the units digit of the question

7^4=1( last digit) 7^5=7( last digit)

Hence, 1\times 7 =7

7 to the 4th power ends in 1 and 7 to the 5th power ends in 2, and 1 times 7 = 7, the last digit of 117 to the 4th power times 347 to the 5th power.

7x7=49 7x7=49 9x7=63 3x7=21 1x7=7 Multiplicando o valor correspondente das casas de unidade equivalentes a cada expoente temos que 1x7=7 ou seja, não importa o valor que de o algarismo , a casa da unidade será igual a 7 e cada numero tem uma sequencia dessas ,que forma um ciclo após uma determinada elevação dele por ele mesmo , Obs: qualquer numero inteiro real!

the units digit of 117^4 X 347^5 = the units digit of 7^4 X 7^5. The unit digit of 7^4 is 1 and of 7^5 is 7...so 1X7 =7....so 7 is the answer.

1*7 = 7