Table of Contents
How do you find the last two digits of a large exponent?
Case 2: Units digit in x is 3, 7 or 9
- When x ends in 9.
- Raise the base by 2 and divide the exponent by 2 =>
- Number ending in 9 raised to 2 ends in 1 =>
- When x ends in 3.
- Raise the base by 4 and divide the exponent by 4 =>
- Number ending in 3 raised to 4 ends in 1 =>
- When x ends in 7.
How do you calculate 2 raise to the 30 power?
If you do all the multiplication, you’ll find that 2 to the 30th power equals 1,073,741,824!
How do you find the power of big numbers?
Here is the algorithm for finding power of a number….Multiply(res[], x)
- Initialize carry as 0.
- Do following for i=0 to res_size-1. …. a. Find prod = res[i]*x+carry. …. b. Store last digit of prod in res[i] and remaining digits in carry.
- Store all digits of carry in res[] and increase res_size by number of digits.
What is 2 by the power of 20?
1048576
Answer: 2 to the power of 20 is 1048576.
How do you calculate 2 to the power of 40?
- 2^40 = (2^10)^4 = (1000+24)^4. Using binomial expansion =
- = 1000^4 + 96(1000)^3 + 3456(1000)^2 + 55296(1000) + 331776.
- = 1000000000000+96000000000+3456000000+55296000+331776.
- = 1,099,511,627,776.
How do you find the power of a number efficiently?
- # Naive iterative solution to calculate `pow(x, n)`
- def power(x, n):
- # initialize result by 1.
- pow = 1.
- # multiply `x` exactly `n` times.
- for i in range(n):
- pow = pow * x.
- return pow.
How to find the last two digits of number raised to power?
How to find the Last Two Digits of Number raised to Power. Let the number be in the form ${x^y}$. Based on the value of units digit in the base i.e x, we have four cases. Case 1: Units digit in x is 1. If x ends in 1, then x raised to y, ends in 1 and its tens digit is obtained by multiplying the tens digit in x with the units digit in y.
How do you find the power of two numbers with different exponents?
Powers of two that differ in their exponents by 4·5 m-1 have the same ending m digits. There are two ways to use the cycle information, in techniques I call the table method and the base power method. In the table method, you compute the powers of two mod 10 m in sequence, until the ending digits cycle.
What is the set of last digits of powers of powers?
The set of last digits of powers forms a periodic sequence with periods given by the table below: 7^ {358} 7358. Notice the pattern of the last digits. They are 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, … 7,9,3,1,7,9,3,1,7,9,\\ldots 7,9,3,1,7,9,3,1,7,9,….
How do you find the base power of two?
You can find the base power of two directly: it is 2 m + j, where j is an offset given by the expression n-m (mod 4·5 m-1 ). For example, let’s find the last digit of 2 2009. , so the base power of two is 2 1+0 = 2 1 = 2. Trivially, we can see the ending digit is 2. For the last two digits of 2 2009, compute .