Exponent Laws Practice: Simplifying Fractional Exponents

[Nelo]

Homework Statement

2^-4 + 2^-6
_____________
2^-3

Homework Equations

The Attempt at a Solution

Ive tried several times, I do the reciprical of all numbers

ie) 1/2^4 + 1/2 ^6
___________________
2^3

Which gives me The wrong answer, cause i do the addiition first, finish all the powers and can't get the right answer. The book shows the next step to be...

2^2 + 1
________
2^6

Which i don't get

 

[eumyang]

Don't rewrite the expression with positive exponents. (You did it wrong, anyway.) Instead, multiply the numerator and denominator by 2⁶.

 

[Nelo]

wat..? Dont make them positive yet multiply them with a positive denom. ? I don't even understand how the person got to 2^6.

 

[eumyang]

It would also be helpful if you can check your original problem for typos. Because the problem you state:
$$\frac{2^{-4} + 2^{-6}}{2^{-3}}$$
does not equal the answer you state:
$$\frac{2^{2} + 1}{2^{6}}$$

wat..? Dont make them positive yet multiply them with a positive denom. ?

Sure, why not? If the original problem you stated was typed correctly, then I would multiply numerator by denominator by 2⁶, because 2^-6 is the smallest power of 2. 2^-6 * 2⁶ = 1, after all.

If you look at this similar example:
$$\frac{5^{-7} + 5^{-2}}{5^{-5}}$$
I would multiply top and bottom by 5⁷ because 5^-7 is the smallest power shown.