Question

What is the unit digit in the product (14)^{153} (23)^{84} (625)^{72}?0123

Answer 1

Answer:

14^153 varies with odd and even number

when exponent is odd unit digit 4

when even unit digit 6

23^84

when power 1 units digit 3

2 9

3 7

4. 1

this will continue

so for power 84 units digit 1

for 625^72

625^1. units digit 5

625^2. 5

also for 625^72 units digit 5

multiply all unit digits

we will get the answer 0

Answer 2

Answer : 0

Explanation :

Unit digit in the product is The product of unit digits in individual terms.

So, To find the unit digit in (14)^{153} × (23)^{84}× (625)^{72} , We need to find unit digits individually and Multiply them over.

So, 14^453

• Unit digit is 4
• It is powered to 453
• Odd power of 4 yields unit digit 4
• Even power of 4 yields unit digit 6.
• Power 453 is odd, so it gives unit digit as 4.

Therefore, Unit digit of 14^453 = 4

Now, (23)^{84}

• Unit digit is 3
• It is powered to 84
• We know that,
• We know that, Unit digits of 3 repeats themselves after 4 time. That is, 3^1 has the same unit digit as 3^4n + 1
• So, 3^84 = 3^4(20)+4
• Unit digit = Unit digit of 3^4 = Unit digit of 81 = 1

Therefore, Unit digit of 3^84 = 1

Now,

625^{75}

• Unit digit is 5.
• It's powered to 75
• We know that, Any Power of 5 yields unit digit 5.

Therefore, Unit digit of 625^75 is 5

Unit digit of the product ; (14)^{153} × (23)^{84}× (625)^{72}

= Unit digit of 4 × 1 × 5

= Unit digit of 20

= 0

Unit digit of the product is 0

Hence, 0 is the required answer!