What will be the unit digit of \({64^{{{128}^{256}}}}\)?1. 22. 43. 64.

1.	What will be the unit digit of \({64^{{{128}^{256}}}}\)?1. 22. 43. 64. 8
Answer» Correct Answer - Option 3 : 6 Given: The given expression is \({64^{{{128}^{256}}}}\) Concept Used: Concept of unit digit Calculation: The given expression can be written as 64^{128 × 128 × 128………… × 256 times} Again the expression can be simplified as 64^{128 × (128 × 128 × 128………… × 255 times)} 64^{128 × (128 × 128 × 128………… × 255 times)} = 64^{4 × 32 × (128 × 128 × 128………… × 255 times)} Now, let 32 × (128 × 128 × 128………… × 255 times) = n 64^{4 × 32 × (128 × 128 × 128………… × 255 times)} = 64^{4 × n} Now, unit digit of 64^{4 × n} 64^{4 × n} = (4)^{4 × n} For any value of n 4^{4 × n} always gives the unit digit as 6 ∴ The unit digit is 6.

What will be the unit digit of \({64^{{{128}^{256}}}}\)?1. 22. 43. 64. 8

Answer» Correct Answer - Option 3 : 6

Given:

The given expression is \({64^{{{128}^{256}}}}\)

Concept Used:

Concept of unit digit

Calculation:

The given expression can be written as 64^{128 × 128 × 128………… × 256 times}

Again the expression can be simplified as 64^{128 × (128 × 128 × 128………… × 255 times)}

64^{128 × (128 × 128 × 128………… × 255 times)} = 64^{4 × 32 × (128 × 128 × 128………… × 255 times)}

Now, let 32 × (128 × 128 × 128………… × 255 times) = n

64^{4 × 32 × (128 × 128 × 128………… × 255 times)} = 64^{4 × n}

Now, unit digit of 64^{4 × n}

64^{4 × n} = (4)^{4 × n}

For any value of n 4^{4 × n} always gives the unit digit as 6

∴ The unit digit is 6.

Discussion

No Comment Found

Related InterviewSolutions

If the remainder when 2x3 + 3x2 – 5kx + 15 is divided by x – k is 2k3, then find the value of k.1. ±√(15/2)2. ±√(5/2)3. ±√154. ±√2
Find the value of k for which the roots are real and equal in the following equation:Kx2 – 2√5x + 4 = 0 1. 5/42. √53. 2√34. 4/5
If x2 - 5x + 1 = 0, then the value of \(\left(x^4 + \frac 1 {x^2}\right) \div \left(x^2 + 1\right)\) is:1. 252. 213. 224. 24
यदि `x=3+2sqrt(2)` और `xy=1` है तो `(x^(2)+3xy+y^(2))/(x^(2)-3xy+y^(2))` का मान ज्ञात करें।A. `30/31`B. `70/31`C. `35/31`D. `37/31`
Salary of 2 teachers and 4 peons is 28000 rupees, whereas salary of 2 teacher and 7 peon is 34000 rupees, then find out the salary of a teacher.1. 80002. 90003. 100004. 11000
If a2x + b2y + c2z = 9x + 121y + 81z, where a, b, c are positive integers, then find the value of c + a - b1. 12. -313. -14. 5
If x + y = 5 and xy = 6, find the value of x - y. Given that x > y1. 12. 213. -14. 13
A spends Rs. 56,000 to purchase a certain number of laptops. The price of one laptop is Rs. 2,000. If the price of a laptop rises by 75%. Then find how many laptops should be purchased less so that the expenditure should remain constant.1. 102. 123. 254. 15
A kurta cost Rs. 12 more than the cost of a shirt. The total cost of 2 such Kurtas and 5 such shirts is Rs. 234. The cost of 3 shirts is: 1. Rs. 902. Rs. 423. Rs. 304. Rs. 60
In the given question, two equations numbered I and II are given. Solve both the equations and mark the appropriate answer.I. x2 - 7x + 12 = 0II. y2 - 5y + 6 = 01. x > y2. x < y3. x ≥ y4. x ≤ y5. x = y or the relationship between x and y can not be established.