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i am very confused how to simplify this considering there is addition (and not multiplication) of negative exponents in both numerator and denominator.

$$\frac{8^{-4/3} + 2^{-2}}{16^{-3/4}+2^{-1}}$$

Since there is addition, i cannot just do the reciprocal of the fraction to remove the negative from the exponents, so how is one supposed to solve this?

user1078
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1 Answers1

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got it from the comments!!! fraction converted to power of 2 simplifies to:

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

then i take common factor:

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

results in $$\frac{1}{2}$$

user1078
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    The idea usually is to look for the most common "elements". In this case, converting all expressions to power of 2 works. – NoChance May 23 '23 at 09:33
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    Nice, I don't think I would have noticed that common factor. I would have multiplied by $\frac{2^4}{2^4}$ to get rid of the negative exponents, giving $\frac{2^0+2^2}{2^1+2^3}=\frac{5}{10}=\frac{1}{2}$. – Jaap Scherphuis May 23 '23 at 11:10