Simplifying exponents, multiplication, and addition

Question

How can you get $10^{n+1}$ from $9\cdot 10^n+10^n$? This is part of a proof I am working on.

Gerry Myerson · Accepted Answer · 2012-03-01 22:37:36Z

up vote 2 down vote accepted

Start with the distributive law.

answered Mar 1 '12 at 22:37

Gerry Myerson
85.8k462141

Wow I totally did not think of that. I thought it would be much more difficult. Thanks! – Izzy Ward Mar 1 '12 at 22:40

Ilmari Karonen · Answer 2 · 2012-03-02 01:09:26Z

up vote 1 down vote

$$\begin{aligned} 9 \cdot 10^n + 10^n &= (10-1) \cdot 10^n + 10^n \\ &= 10 \cdot 10^n - 10^n + 10^n \\ &= 10^{n+1} \end{aligned}$$

edited Mar 2 '12 at 1:09

Ilmari Karonen
8,2261534

answered Mar 1 '12 at 22:42

Mia
26117

Another way is $9 \cdot 10^n + 10^n = (9 + 1) \cdot 10^n = 10 \cdot 10^n = 10^{n+1}$. – Ilmari Karonen Mar 2 '12 at 1:11

2 Answers