SOLUTION: Hi, i know this question has already been answered but i did not understand how they got the answer. Simplify: 3^(n-1)+3^(n-1)+3^(n-1) This is their working out: 3[3^(n-1)]

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Question 1026256: Hi, i know this question has already been answered but i did not understand how they got the answer.
Simplify:
3^(n-1)+3^(n-1)+3^(n-1)
This is their working out:
3[3^(n-1)]
3^(n-1+1) <-- i'm not sure how they got +1 and isn't 3[3^(n-1)]= 9^(n-1)? , can you explain please?
=3^n
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Number Statement Reason

1. 3^(n-1)+3^(n-1)+3^(n-1) NA

2. 3 * [3^(n-1)] Combine like terms

3. 3^1 * [3^(n-1)] Rewriting the first '3' as '3^1'

4. 3^[1+(n-1)] Using the rule x^y*x^z = x^(y+z)

5. 3^(1-1+n) Associative and commutative properties of addition

6. 3^(0+n) Combine like terms

7. 3^n Use the rule 0+x = x

So in the end, 3^(n-1)+3^(n-1)+3^(n-1) simplifies to 3^n

The final answer is 3^n