Math Problem Statement
The digit in the U it's place of the number represent by (7^95-3^58) is
Solution
To find the digit in the units place of the number represented by , we need to determine the units digit of both and individually, and then subtract the second from the first.
Step 1: Determine the units digit of
The units digits of powers of 7 follow a cycle:
So the cycle of the units digits is , repeating every 4 terms.
To find the units digit of , we calculate the remainder when 95 is divided by 4:
Thus, the units digit of is the same as the units digit of , which is 3.
Step 2: Determine the units digit of
The units digits of powers of 3 follow a cycle:
So the cycle of the units digits is , repeating every 4 terms.
To find the units digit of , we calculate the remainder when 58 is divided by 4:
Thus, the units digit of is the same as the units digit of , which is 9.
Step 3: Subtract the units digits
Now, subtract the units digit of from the units digit of :
Since we want the units digit, we take this modulo 10:
So, the units digit of is 4.
Would you like more details or have any questions? Here are some related questions you might find interesting:
- How do you find the units digit of large exponents efficiently?
- What is the significance of the modulo operation in finding units digits?
- Can you calculate the last two digits of ?
- How do units digits cycles differ between different numbers?
- What are the properties of modular arithmetic in the context of large numbers?
Tip: Understanding patterns in units digits for powers is a powerful tool in solving many exponent-related problems!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Exponentiation
Modular Arithmetic
Units Digits
Formulas
-
Theorems
-
Suitable Grade Level
High School