Answer:
The values of a and b in the prime decomposition of 136 are a = 3 and b = 17.
Explanation:
To find the prime decomposition of 136, we need to express it as a product of prime numbers. Let's start by finding the prime factors of 136.
The prime factorization is the process of expressing a number as a product of its prime factors.
We'll divide 136 by prime numbers until we can't divide it any further.
Starting with the smallest prime number, which is 2:
136 ÷ 2 = 68
We can divide 68 by 2 again:
68 ÷ 2 = 34
And we can divide 34 by 2 again:
34 ÷ 2 = 17
Now, we have reached a prime number, 17. So the prime factorization of 136 is:
136 = 2 × 2 × 2 × 17
To express this in the form 2^a x b, we can rewrite it as:
136 = 2^3 x 17
Therefore,
a = 3 and b = 17.