Find the unit digit of (330 - 245).

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Find the unit digit of (330 - 245).

Asked on 2019-05-25 14:31:20 by Guest | Votes 0 | Views: 22 | Tags: cbt | miscellenaeous | Add Bounty

Find the unit digit of (3³⁰ - 2⁴⁵).
1). 1
2). 3
3). 5
4). 7

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Answered by Guest on 2019-05-25 14:56:50 | Votes 0 | #

We know, 3⁵ = 243

We can write,

⇒ Unit digit of 3³⁰ = Unit digit of (3⁵ × 3⁵ × 3⁵ × 3⁵ × 3⁵ × 3⁵) = Unit digit of (3 × 3 × 3 × 3 × 3 × 3)

⇒ Unit digit of 3³⁰ = Unit digit of (729) = 9

Similarly, 2⁵ = 32, 2¹⁰ = 1024

We can write,

⇒ Unit digit of 2⁴⁵ = Unit digit of (2¹⁰ × 2¹⁰ × 2¹⁰ × 2¹⁰ × 2⁵) = Unit digit of (4 × 4 × 4 × 4 × 2)

⇒ Unit digit of 2⁴⁵ = Unit digit of (512) = 2

∴ Unit digit of (3³⁰ - 2⁴⁵) = 9 - 2 = 7

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