Question

2^(2k-1)*3^(2k-1)/12*6^(2k-2)

Answer 1

2^(2k - 1) * 3^(2k-1) = 6 ^ (2k - 1)

6 ^(2k - 2)  = 6^(2k - 1) / 6

Итого :

2^(2k-1)*3^(2k-1)/12*6^(2k-2) = 6^(4k - 2)/ 12 = 6^(4k - 3) / 2

Answer 2

To simplify the expression 2^(2k-1) * 3^(2k-1) / (12 * 6^(2k-2)), we can first simplify the denominator and then cancel out common factors from the numerator and denominator.

Let's start by simplifying the denominator: 12 = 2 * 6 6^(2k-2) = (2*3)^(2k-2) = 2^(2k-2) * 3^(2k-2)

So, the denominator becomes: 12 * 6^(2k-2) = (2 * 6) * (2^(2k-2) * 3^(2k-2)) = 2^(1 + 2k-2) * 3^(1 + 2k-2) = 2^(2k-1) * 3^(2k-1)

Now, let's rewrite the expression with the simplified denominator: 2^(2k-1) * 3^(2k-1) / (2^(2k-1) * 3^(2k-1))

Since the bases (2 and 3) are the same, you can subtract the exponents in the denominator from the exponents in the numerator:

(2^(2k-1) * 3^(2k-1)) / (2^(2k-1) * 3^(2k-1)) = 1

So, the simplified expression is 1.