Understanding Exponents: Multiplying 10 to the Power of 3 Explained

[Mr_Bojingles]

Does 10 to the power of 3 = 1,000 or 10,000? To calculate is do I multiply 10x10=100 then 100x100=10,100 or do I multiply 10x10=100 then 100x10=1,000?

I know this is a really stupid question but its been a long time since I did basic maths and I've forgotten how this stuff works.

 

[symbolipoint]

"Power" means "exponent".

Ten to the power of three means $$\[<br /> 10^3 <br /> \]$$

 

[bjgawp]

$$a^{n} = \underbrace{a \cdot a \cdot a \cdot a \cdot \: ... \: \cdot a \cdot a}_{\mbox{n times}}$$

$$10^{3} = 10 \cdot 10 \cdot 10$$

Whether you noticed it or not:
$$10^{1} = 10$$
$$10^{2} = 100$$
$$10^{3} = 1000$$
$$10^{n} = 1\underbrace{0000 \: ... \: 00}_{\mbox{n zeroes}} \quad \mbox{n \geq 0}$$

 

[CompuChip]

Also works the other way
$$10^0 = 1$$ (a 1 with no zeroes)
$$10^{-1} = 0,1$$
$$10^{-2} = 0,01$$
$$10^{-n} = \underbrace{0,00\ldots000}_{n \text{ zeroes}}1$$

 

[homeworkhelp]

It is definitely 1000, how did you get 10000 ?

 

[JasonRox]

It is definitely 1000, how did you get 10000 ?

Maybe he thought, take 10 and add 3 zeroes. That is 10000.

 

[CompuChip]

As he said in the first post,

do I multiply 10x10=100 then 100x100=10,100 or do I multiply 10x10=100 then 100x10=1,000?

and the answer is of course, you multiply
10 x 10 x 10 = (10 x 10) x 10 = 100 x 10 = 1000
just like
2^5 = 2 x 2 x 2 x 2 x 2 = (2 x 2) x (2 x 2) x 2 = 4 x 4 x 2 = (4 x 4) x 2 = 16 x 2 = 32
and not
2 x 2 = 4
4 x 4 = 16
16 x 16 = 256
256 x 256 = 65 536
65 536 x 65536 = 4 294 967 296
or something like that

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[Mr_Bojingles]

Thanks a lot. I couldn't remember if it was 10x10x10 or 10x10x100. I was thinking it might have meant multiplying it by itself the amount of times the exponent indicates. For example 10 to the power of 5 I thought it might have been 10x10x100x1000x10000

 

[CompuChip]

Nope, a^n is just notation for multiplying a with itself n times, just like n x a is notation for adding it to itself n times.

10x10x100x1000x10000 would be (10) x (10) x (10 x 10) x (10 x 10 x 10) x (10 x 10 x 10 x 10) = (counting the 10's in there) 10^11.