How many n-digit numbers are there in which only digits used are 1 to

A quick approach is to test some values

For example, let's see what happens with n = 1
So, the question becomes "How many 1-digit numbers are there in which only digits used are 1 to 9 (excluding 0) and no two consecutive digits are same?"
Well, there are 9 such numbers: 1, 2, 3, 4, 5, 6, 7, 8, and 9
So, when n = 1 the answer to the question is 9

Now plug n = 1 into each answer choices and see which ones yield an output of 9
We get:
(A) 9 x 8^1 = 72. No good. We want an output of 9. ELIMINATE
(B) 9 x 8^(1-1) = 9. Great! Keep.
(C) 9^(1-1) = 1. No good. We want an output of 9. ELIMINATE
(D) 9^1 = = 9. Great! Keep.
(E) 8^1 = 8. No good. We want an output of 9. ELIMINATE

We're left with just B and D
So, we must test another value of n

Let's see what happens with n = 2
So, the question becomes "How many 2-digit numbers are there in which only digits used are 1 to 9 (excluding 0) and no two consecutive digits are same?"
Well, there are 9 options for the first digit
And there are 8 options for the second digit
So, the total number of integers that meet the give conditions = 9 x 8 = 72
So, when n = 2 the answer to the question is 72

Now plug n = 2 into each answer choices and see which ones yield an output of 72
We get:

(B) 9 x 8^(2-1) = 72. PERFECT!!
(D) 9^2 = 81. No good. We want an output of 72. ELIMINATE

Answer: B

Cheers,
Brent