Question

The digit in the unit’s place of \[{5^{834}}\] is
A. \[0\]
B. \[1\]
C. \[3\]
D. \[5\]

Answer 1

Hint: In this question, we need to find the unit place of the given number. For that, it is sufficient to find the given number's square and cube to obtain the desired result.

Complete step-by-step solution:
We are given a number \[{5^{834}}\]
Now we see that the given number has only one digit which is \[5\]
Now the square of the given number \[5\] is:
\[
  {5^2} = 5 \times 5 \\
   = 25
 \]
Thus, the unit digit place of the number \[25\] is \[5\]
Now the cube of the given number \[5\] is:
\[
  {5^3} = 5 \times 5 \times 5 \\
   = 125 \\
 \]
Thus, the unit digit of the number \[125\] is \[5\].
So we can say that any odd or even power of 5 will give us a number with unit’s digit 5.
Therefore, the digit in the unit’s place of \[{5^{834}}\] is \[5\].
Hence, option (D) is the correct

Additional information: To solve these types of questions, remember the seven basic exponent rules or the laws of exponents. Make sure to read the following rules, which explain how to solve different types of exponent problems and how to add, subtract, multiply, and divide exponents: Powers rule as a product, power quotient rule, power rule, product rule power, quotient rule's power, rule of zero power, negative exponent rule

Note: To solve this type of question, remember that finding the unit digit of the square of the number '1234' is as simple as finding the unit digit of the square of the unit digit of the given number because the unit digit is only dependent on the unit digit's place in any operation, regardless of the other numbers.