10^100 and so on.

[Penumbra]

Hi, I am 100% new to all of these boards. I have been drawn here because I saw a science forum, and inside of that an astronomy and cosmology forum (!). I thought it would be better to ask here, and not in science for my question about scientific notation.

 

I remember learning about this, a long time ago, but I have forgotten, and need help. =\ Is there any easy way (minus using a calculator) to solve equations such as 26^78 or 13^90 and so on? I'm just making up these numbers at random, so please be gentle.

 

I appreciate any help!

[Lyssia]

(Apologies in advance if this isn't of much help - today's been exhausting )

 

I think it depends on what you need to do with them. In my first algebra course at uni we learnt one way of simplifying them just for the sake of making the expression easier to swallow (and usually the answer dropped out nicely if you'd done it right).

[matt grime]

Is there any easy way (minus using a calculator) to solve equations such as 26^78 or 13^90 and so on?

 

What do you mean by solve? (nb there are no equations there; equations are characterized by having equals signs in them)

[Penumbra]

Well then, how do you solve 26 to the power of 78, other than calculating 26x26(etc) 77 more times? What exactly is 32^47 as a solid number? For your pleasure, I have not learned 100% English yet, as I am not from here, I am also horrible at math, please don't penalize me. =/

[NeonBlack]

he means 'evalute expressions' rather than 'solve equations'

[matt grime]

I am not penalizing you I am asking you to clarify what you meant since the words you use have a strict mathematical meaning different from your usage of them.

 

There may be some tricks, some short cuts, but if you really have to write it out in base 10 then you just have to get on and do it. Why should it be any other way? Have a big bit of paper handy though.

[BigMoosie]

Even your regular calculator will not be able to evaluate these expressions.

[bmaxwell]

I think the confusion is that the examples given are not scientific notation they are infact just numbers albiet very very large numbers.

 

Scientific notation would be something like 26 x 10^78

In this case there is a simple way to find this number with out all the fuss and hub bub of carots and the like.

 

Just move the decimal 78 places to the right.

 

Ofcourse I think in scientific notation a lowercase E is used.

 

My calculator approximates all numbers this way.

 

26.00 e 78

 

something like that.

[insane_alien]

26 x 10^78 thats not the same number as 26^78 a big bit of paper would be very handy for this. what the heck, i'm bored i'll just go do it.

[insane_alien]

Ok after a bit of working out i have concluded that i am not actually THAT bored at all i just thought i was. I'm off for the thrills of staring at a wall.

[DQW]

26 x 10^78 thats not the same number as 26^78 a big bit of paper would be very handy for this. what the heck, i'm bored i'll just go do it.

It doesn't take more than a small post-it note if you have a slide-rule or a century-old calculator...

 

[math]26^7 \approx 8*10^9 ~ \implies 26^{78} \approx 26*8^{11}*10^{99} [/math]

that took a calculator, but it could be avoided too (with bigger paper)

[math]8^3 \approx 500 \implies 8^{11} \approx \frac{5^4*10^8}{8} \approx 8*10^9 [/math]

[math]\implies 26^78 \approx 8*26*10^{108} \approx 2.1*10^{110} [/math]

 

According to the Google calculator :

26^78 = 2.3330344 × 10¹¹⁰

[doomtiki]

A more powerful calculator could easily evaluate such expressions exactly. Try using an HP-49g+ or use the free computer algebra system Maxima. I have used Maxima to evaluate things as large as 128^65536. Unfortunately, I do not think there is a fast method to evaluate random exponents of random numbers manually.