Answer: Check
12^10 × 12^(-2) = 12^(10 - 2) = 12^8
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Second option : ---
3^2 × 4^6 = 3^2 × 4^2 × 4^4 = 12^2 × 4^4
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Third option : ---
(12^8)^0 = 12^(8 × 0) = 12^0 = 1
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4th option : Check
12^10 / 12^2 = 12^10 × 12^(-2) = 12^(10 - 2)
= 12^8
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5th option : Check
2^8 × 6^8 = ( 2 × 6 )^8 = 12^8
Step-by-step explanation:
First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.
We have
130 = 2 • 5 • 13
231 = 3 • 7 • 11
so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.
To verify the claim, we try to solve the system of congruences

Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:
130 = 7 • 17 + 11
17 = 1 • 11 + 6
11 = 1 • 6 + 5
6 = 1 • 5 + 1
⇒ 1 = 23 • 17 - 3 • 130
Then
23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)
so that x = 23.
Repeat for 231 and 17:
231 = 13 • 17 + 10
17 = 1 • 10 + 7
10 = 1 • 7 + 3
7 = 2 • 3 + 1
⇒ 1 = 68 • 17 - 5 • 231
Then
68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)
so that y = 68.
Answer:
d 70%
Step-by-step explanation:
30 students in class
21 students with 5+ vowels
21/30 x 100 = 70%
The absolute value is 18.26