Question

How do you solve `(2^6 times 2^3)/(2^n) = 2^5`?

Answer 1

`n=4`

Explanation:

First multiply both sides by `color(green)2^color(green)n` :

`(2^6 times 2^3)/(2^n)` `times` `color(green)2^color(green)n` `=` `2^5` `times` `color(green)2^color(green)n`

This will remove `2^n` from the LHS :

`(2^6 times 2^3)/cancel(2^n)` `times` `cancel(2^n)` `=` `2^5` `times` `color(green)2^color(green)n`

Second add the exponents of similar bases :

`2^(6+3)` `=` `2^(5+n)`

`=>` `2^9` `=` `2^(5+n)`

Third use the `"Base Rule"` :

i.e. `9= 5 + n`

`:.` `n=4`