Question

What is the unit digit in the product (3547)153*(251)72

Answer 1

You need the unit digit in (3547)^153*251^72.

Take first expression: (3547)^153

Step 1: Take the unit digit of base = 7:

Step 2: Check it's periodicity-:

7^1=7

7^2=49 (last digit=9)

7^3=343 (last digit=3)

7^4=> last digit=1

7^5=> last digit=7

Hence periodicity of 7=4, since after that digits repeat again.

Step 3: calculate power modulus periodicity:

pmp = 153%4=1

Step 4: answer is last digit of base to the power pmp calculated in step 3:

7^1= 7 is the last digit

Step 5: Repeat same for 2nd and other expressions.

Last digit of (251)^72 is 1. Since periodicity of 1 is 1.

Step 6: Multiply results of all expressions:

Answer= 7*1=7.

Answer 2

Answer:

Unit digit = 7