Video summary

Rajasthan Computer Anudeshak Bharti 2026 | Maths Class – संख्या पद्धति (Number System) Part 14

Main summary

Key takeaways

Educational

Main ideas and lessons (Unit Digit of Powers)

  • The class focuses on finding the unit digit (last digit) of numbers written in power/exponent form.
  • Earlier parts covered unit digit patterns for products/multiplications; today extends to exponents.
  • Core challenge: you can’t compute huge powers directly—so you use remainder/pattern rules instead.

Method / Rules taught

A) Unit digit when the base is raised to a large power (the “divide by 4” approach)

For problems like:

  • ((\text{base})^{\text{exponent}})

you don’t compute the full power. Instead:

  1. Find the unit digit pattern of the base.
    • Unit digits repeat in a cycle of length 4.
  2. Locate the exponent in that cycle:
    • Divide the exponent by 4
    • Take the remainder
  3. Use the remainder to determine the effective smaller exponent:
    • If the remainder is (r), compute only ( \text{base}^r ) for unit digit purposes.
  4. Special case: remainder = 0
    • If the exponent is divisible by 4 (remainder (0)), treat the effective exponent as 4.

B) Why “4” is used (conceptual reason)

  • The unit digit of powers of a number repeats every 4 steps.
  • Example (conceptually):
    • For base 2: (2^1, 2^5, 2^9,\dots) share the same unit digit.
  • The presenter generalizes that a repeating cycle of length 4 applies to unit digits for any base.

C) Shortcut rules for bases with fixed unit digits

If the unit digit of the base is 0, 1, 5, or 6, then:

  • The unit digit never changes, no matter the exponent.

So:

  • If a number ends in 0, (x^k) ends in 0
  • If it ends in 1, (x^k) ends in 1
  • If it ends in 5, (x^k) ends in 5
  • If it ends in 6, (x^k) ends in 6

D) Special cycles for bases ending in 4 and 9

Base ends in 4:

  • Exponent even → unit digit = 6
  • Exponent odd → unit digit = 4

Base ends in 9:

  • Exponent even → unit digit = 1
  • Exponent odd → unit digit = 9

E) Handling expressions with multiple power terms (addition/subtraction)

For expressions like:

  • (A^p \pm B^q \pm \dots)

Approach:

  • Compute the unit digit of each power term separately using the rules above.
  • Then do the final (+) or (-) operation on the unit digits only.
  • If subtraction “goes below 0”:
    • Don’t treat negative unit digits literally—ensure the final unit digit is a valid 0–9 result.

Example problem types shown

  • Expressions such as (9^{97} + 27^9) (and similar), where:
    • exponent reduction via mod 4 is used
    • parity rules for bases ending in 9/4 are highlighted
  • Problems involving addition/subtraction of multiple terms, where only the unit digits matter.
  • Problems where bases have unit digits in {0, 1, 5, 6}, used as immediate shortcuts.
  • A trick-style case where terms cancel/combine so that only one effective unit digit outcome remains.

Test-taking / learning guidance emphasized

  • Regularity: don’t miss classes (especially Monday).
  • Consistency / concentration: focus during study; don’t get distracted.
  • Mentions the strategy of not trying to solve 100% of the paper—sometimes leaving a few questions can help overall.

Speakers / sources featured

  • Main speaker (teacher): “Sir” (unnamed in subtitles; addressed as Kabra ji by the audience/host moments)
  • Students/audience participants (named in subtitles):
    • Priyanka ji
    • Darshan ji
    • Sunny ji
    • Manisha ji
    • Madhav ji
    • Prashant ji
    • Chaudhary sahab
    • Pankaj Sir (mentioned for a different marathon session)
  • The host/program does not explicitly name any official source beyond the teacher and students.

Original video