Comparing Exponentiation: 20^100 vs. 400^40?

[pandamonium786]

Homework Statement

Without using a calculator and without evaluating expressions, determine which is greater. 20^100 or 400^40

Homework Equations

None, however some exponent laws and possibly mental math are applicable.

The Attempt at a Solution

I don't know how to reach an answer without some type of evaluation; which goes against the question.

 

[berkeman]

Homework Statement

Without using a calculator and without evaluating expressions, determine which is greater. 20^100 or 400^40

Homework Equations

None, however some exponent laws and possibly mental math are applicable.

The Attempt at a Solution

I don't know how to reach an answer without some type of evaluation; which goes against the question.

You should at least put forth some guesses. Hint -- what can you say about how many zeros will be in each answer?

 

[Bystander]

without some type of evaluation

Write 400 in terms of 20.

 

[pandamonium786]

You should at least put forth some guesses. Hint -- what can you say about how many zeros will be in each answer?

I don't know if i am right, but would there be 3 0's in 20^100 and around 4 0's in 400^40?

 

[pandamonium786]

Write 400 in terms of 20.

What do you mean?

 

[berkeman]

I don't know if i am right, but would there be 3 0's in 20^100 and around 4 0's in 400^40?

No. Please review how exponents work.

10^2 = 10*10 = 100

10^3 = 10*10*10 = 1000

...and so on...

 

[Bystander]

What do you mean?

Can you relate "400" to "20" or "20" to "400?" Are there some simple operations you can perform on either number to get the other?

 

[pandamonium786]

Can you relate "400" to "20" or "20" to "400?" Are there some simple operations you can perform on either number to get the other?

well 20 x 20 = 400 or 400/20 = 20

 

[Bystander]

well 20 x 20 = 400

Give you any ideas?

 

[pandamonium786]

Give you any ideas?

Does that mean that since 20^2 = 400 the 400^40 has to be greater than 20^100. Since 400^2 alone is approximately greater than 20^2.

 

[Ray Vickson]

Does that mean that since 20^2 = 400 the 400^40 has to be greater than 20^100. Since 400^2 alone is approximately greater than 20^2.

No, it does not mean that; it is not even true.

 

[Bystander]

You're playing with the right ideas, but do what Berkeman has recommended regarding laws of exponents; N^{(k x j)} = (N^k)^j .

 

[pandamonium786]

No, it does not mean that; it is not even true.

then what do you propose the answer is and how would you get to it?

 

[pandamonium786]

P

You're playing with the right ideas, but do what Berkeman has recommended regarding laws of exponents; N^{(k x j)} = (N^k)^j .

Please expand. Also how would you reach the answer logically?

 

[Bystander]

Please expand

I'll nudge you in the direction you need to go, but you have to do the work.
Take what you did earlier,

20^2 = 400

pick some values for N, j, k and put them into the general statement I gave you for one of the laws of exponents.

N(k x j) = (Nk)j

 

[pandamonium786]

I'll nudge you in the direction you need to go, but you have to do the work.
Take what you did earlier,

pick some values for N, j, k and put them into the general statement I gave you for one of the laws of exponents.

So would 400^40 be greater because

I'll nudge you in the direction you need to go, but you have to do the work.
Take what you did earlier,

pick some values for N, j, k and put them into the general statement I gave you for one of the laws of exponents.

So that means that 20^100 is actually greater because 20^ 20x20 is bigger than 400^ 20x2.

 

[Bystander]

Quick tutorial on a couple PF features: the Green bar above the reply box will allow you to insert subscripts, x_32n2, or superscripts (exponents), x² or 20¹⁰⁰.
Try redoing what you just did and use this feature --- it might help you visualize just what is "base," (the 20 or the 400) and what is exponent (superscript).

 

[Ray Vickson]

then what do you propose the answer is and how would you get to it?

PF Rules forbid me from telling you the answer. We can give hints only. You have been given plenty of helpful hints already.

 

[Mark44]

Homework Statement

Without using a calculator and without evaluating expressions, determine which is greater. 20^100 or 400^40

Homework Equations

None, however some exponent laws and possibly mental math are applicable.

The Attempt at a Solution

I don't know how to reach an answer without some type of evaluation; which goes against the question.

I don't believe that you are prohibited from doing every calculation - I think that you don't want you to directly calculate 20⁴⁰⁰ and 400⁴⁰. I'm reasonably sure that you are permitted to do some calculations.

 

[berkeman]

Thread closed temporarily to discuss the rules with the OP...