Exponent rules #2

Algebra Level 2

$\large \frac{3 \times 2^n + 4 \times 2^{n+2}}{2^n - 2^{n-1}} = ?$

1 solution

Blan Morrison
Jan 22, 2018

First, we can simplify the expression:

$\frac{3\times2^n+2^{n+4}}{2^{n-1}}$

Then, we can pull out the common term in the numerator:

$\frac{2^n(3+2^4)}{2^{n-1}}$

Simplify:

$2^1(3+16)$

And simplify again:

$2\times19=\boxed{38}$

Why are you setting n = 1 ?

Adrian Ronayne - 3 years, 4 months ago

I didn't. Which step are you talking about?

Blan Morrison - 3 years, 4 months ago

Post first simplify step n is set to 1 . For example 2^n becomes 2^1 ?

Adrian Ronayne - 3 years, 3 months ago

@Adrian Ronayne – Let's ignore the coefficient: $\frac{2^n}{2^{n-1}}$

Because of the rules of exponents, we know that $\frac{a^m}{a^n}=a^{m-n}$

$\frac{2^n}{2^{n-1}}=2^{n-(n-1)}=2^1$

Blan Morrison - 3 years, 3 months ago

Very cute problem :)

MAINAK CHAUDHURI - 3 years, 2 months ago