Write this relationship as a product of powers
One million is 1000 times as great as one thousand

Question

Write this relationship as a product of powers
One million is 1000 times as great as one thousand

mathstudent55 · Answer

10^1 = 10 = 10
10^2 = 10 x 10 = 100
10^3 = 10 x 10 x 10 = 1,000
10^4 = 10 x 10 x 10 x 10 = 10,000
10^5 = 10 x 10 x 10 x 10 x 10 = 100,000
10^6 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000
Does this help?

anonymous · Answer

hmmm

anonymous · Answer

So would it be like 10^6=10^3x10^3?

mathstudent55 · Answer

you got it

anonymous · Answer

Ok cool, but now I have to do a quotient of powers and it doesn't make sense!
One hundred is one-tenth of one thousand

mathstudent55 · Answer

100 = (1/10)(1000)
You need to do it with powers also?

anonymous · Answer

yeah

mathstudent55 · Answer

Remember what I wrote above with 10, 100 etc and the powers of 10?

anonymous · Answer

Yup

mathstudent55 · Answer

You can keep on going to 10^7, 10^8, etc., but you can also go the other way.

mathstudent55 · Answer

10^2 = 10 x 10 = 100
10 = 10 = 10
10^-1 = 1/10 = 1/10
10^-2 = 1/10^2 = 1/100
10^-3 = 1/10^3 = 1/1,000
etc.

mathstudent55 · Answer

You need to write 100 = (1/10)1,000
100 = 10^2
1/10 = 1/10^-1
1,000 = 10^3

anonymous · Answer

ok... I kind of understand What about one is one-millionth of one million

mathstudent55 · Answer

one millionth is 1/1,000,000 = 1/10^6
one million is 1,000,000 = 10^6

anonymous · Answer

Oooh ok

mathstudent55 · Answer

Do you know how to multiply powers with the same base?

anonymous · Answer

Yeah

mathstudent55 · Answer

For example, what is 7^3 x 7^5? without figuring out what each power is

anonymous · Answer

add 3 and 5
so it's 7^8

mathstudent55 · Answer

Ok, since you know that, now look at that example, what is a millionth of a million? Without thinkiong of thise problem and powers, just answer, what is a millionth of a million?

anonymous · Answer

0?

mathstudent55 · Answer

No. If you have a million and take one millionth of it? Think of a similar example with a smaller number. What is a tenth of ten?

anonymous · Answer

1

mathstudent55 · Answer

right. and a millionth of a million is also one.

anonymous · Answer

Oh!

mathstudent55 · Answer

Now think of the example, one millionth of a million using powers of ten
(1/1,000,000)(1,000,000), but we know that 1/1,000,000 is 10^-6 and 1,000,000 is 10^6, so 
(1/1,000,000)(1,000,000) = 10^-6 x 10^6
Using multiplication of powers,
10^-6 x 10^6 = 10^0 = 1
So you see that one millionth of a million is 1whether you do it with numbers or powers of ten

anonymous · Answer

Omg thanks!