Evaluate $2^{-n}(2^n-2^{1+n})$

Question

The answer is $-1$, but how does one expand and simplify this expression to find this answer (what are the steps)?

Distributing that $2^{-n}$ would be a good first step. – Mike Pierce Jun 23 '15 at 19:45 — Mike Pierce, Jun 23 '15 at 19:45

mathlove · Accepted Answer · 2015-06-23T19:59:25.233

8

HINT : $$A(B+C)=AB+AC$$ and$$2^a\times 2^b=2^{a\color{red}{+}b}.$$

edited Jun 23 '15 at 19:59

answered Jun 23 '15 at 19:46

mathlove

Would you please be more direct? I understand this exponent law, but not how to apply it to this situation (expression). – Arthur Alex Karapetov Jun 23 '15 at 19:47
3

@ArthurAlexKarapetov: Can you try to use my hints? – mathlove Jun 23 '15 at 19:49

score 2 · Answer 2 · answered Jun 23 '15 at 19:47

2

$$2^{-n}(2^n-2^{n+1})=2^{n-n}-2^{n+1-n}=1-2=-1$$

answered Jun 23 '15 at 19:47

Thanks a lot! I thought you had to use multiplication of exponents rather than addition, very foolish of me. Thanks again. – Arthur Alex Karapetov Jun 23 '15 at 19:49

2 Answers2