Question

PLEASE SOLVE IT WITH FULL EXPLANATION!!
DONT STEAL POINTS :)​

Answer 1

We are given with a fraction which has a lot of power raised , but their is a way to do it fastly . Consider the given first ;

`{:\implies \quad \sf (2^(30)+2^(29)+2^(28))/(2^(31)+2^(30)+2^(29))}`

Now , here , if we calculate 2³⁰ and the other stuff and then plus and then divide by the stuff in denominator , it will be very long .But here the interesting thing is that , we can see here 28 is the smallest in all powers in both numerator and denominator , but their isn't any 28 raised to 2 in denominator but their is 29 raised to 2 . So , we can take 2 raised to 28 common and then we can cancel it and then it will be very easy for us to calculate it . So , let's proceed

`{:\implies \quad \sf (2^(28)(2^(2)+2^(1)+1))/(2^(28)(2^(3)+2^(2)+2^(1)))}`

`{:\implies \quad \sf \frac{\cancel{2^(28)}(2^(2)+2+1)}{\cancel{2^(28)}(2^(3)+2^(2)+2)}}`

`{:\implies \quad \sf (2^(2)+2+1)/(2^(3)+2^(2)+2)}`

`{:\implies \quad \sf (4+2+1)/(8+4+2)}`

`{:\implies \quad \sf (7)/(14)=\frac12}`

`{:\implies \quad \bf \therefore \quad \underline{\underline{(2^(30)+2^(29)+2^(28))/(2^(31)+2^(30)+2^(29))=\frac12}}}`

Hence , The required answer is ½

Answer 2

Hey there!

2^30+2^29+2^28 / 2^31+2^30+2^29

= 1,073,741,824 + 536,870,912 + 268,435,456 / 2,147,483,648 + 1,073,741,824 + 536,870,912

= 1,610,612,736 + 268,435,456 / 3,221,225,472 + 536,870,912

= 1,879,048,192 / 3,758,096,384

= 1 / 2

≈ 0.50

Therefore, your answer is: 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)