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I have the following question in a practice booklet:

If $\frac{2^{26} - 2^{23}}{2^{26} + 2^{23}}$ = $\frac{x}{9}$ What is $x$?

I know the answer is 7 because it's easy enough when you manually figure out $2^{26}$ etc. but is there a faster way? Can I simplify this down somehow? .

user141562
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  • $$9(2^{26}-2^{23}) = x(2^{26} + 2^{23})$$ $$x = \frac{9(2^{26}-2^{23})}{ {2^{26} + 2^{23}}}$$ – Adola Jan 23 '17 at 13:58

3 Answers3

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$$\frac{2^{26} - 2^{23}}{2^{26} + 2^{23}}=\frac{2^{23}(2^{3} - 1)}{2^{23}(2^3 + 1)}$$

Are you able to complete it?

Siong Thye Goh
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Hint ... start by cancelling the common factor $2^{23}$

David Quinn
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If it is elementary level you should probably learn the rule of the exponents:

$$a^x\cdot a^y = a^{x+y}$$

So the exponents add if we multiply two numbers with the same base $a$ but different exponents. Now you can try and use the rule on your numbers.

mathreadler
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