Find the remainder when 11power50 17power12 is divided by 6
Answers
Answer:
2
Step-by-step explanation:
11≈(-1)mod6
17≈(-1)mod6
11^50+17^12=(-1)^50+(-1)^12=1+1=2
2 is the remainder
1 is the remainder
(11⁵⁰×17¹²)÷ 6 is 1
Step-by-step explanation:
Given:
(11⁵⁰×17¹²)÷ 6 is
To find:
The remainder
Solution:
The exponential term is thus divided by 6, we have to find out the remainder for this value.
⇒ 11⁵⁰×17¹²
6
We expand 17 as (11+6) for calculating the purpose
⇒ 11⁵⁰×(11+6)¹²
6
Thus the powers of the values are written as separate to shorten the value.
⇒ 11⁵⁰×11¹²+6¹²
6
If (yᵃ×yᵇ=yᵃ⁺ᵇ), then distribute the values in this equation we get,
⇒ 11⁵⁰⁺¹²+6¹²
6
⇒ 11⁶²+6¹²
6
The term 11 is expanded as 5+6 for calculation purposes.
⇒ (5+6)⁶²+6¹²
6
The values are evaluating then separate each term.
⇒ 6⁶²+6¹²+5⁶²
6
⇒ 6⁶²+ 6¹² + 5⁶²
6 6 6
The multiplies of 6ˣ are divided by 6,(x maybe 1,2..and so on) in, then the remainder must be 0.
⇒0+0+ 5⁶²
6
Evaluate the term 6 as (5-1) Then the value we get,
⇒(6-1)⁶²
6
Distributing the values of power separately we get,
⇒ 6⁶² - 1⁶²
6 6
Hence,
⇒The remainder is 1.