A kilobyte is 2^10. A megabyte is 2^20 bytes. How many kilobytes are in a megabyte? Use the exponent rule for division to find your answer and give your answer in exponential form.

Question

anonymous · Answer

1mb=2^20b= $$\frac{ 2^{20} }{ 2^{10} }=2^{20}*2^{-10}=2^{20-10}=2^{10}kilobytes$$

anonymous · Answer

so how many kilobytes are in a megabyte and how would i do this?

phi · Answer

surj  gave you the answer in exponential form  (just as the question asks for)

as an aside,  2^10  is 1024,  which is very close to 10^3  (1000)

anonymous · Answer

So what should i put as the answer its an essay question. could you walk me through each step

phi · Answer

give your answer in exponential form.

anonymous · Answer

What surj said, could i use that as the answer

anonymous · Answer

how would i do that?

phi · Answer

yes, but you should understand what he did.

the question says  "Use the exponent rule for division "
that rule is "top exponent minus bottom exponent"

so 2^20  divided by 2^10  means  2^(20-10) (subtract exponents)  to get 2^10

anonymous · Answer

so if its multiplication you add the exponents and if its division you would subtract?

phi · Answer

yes, that is exactly the rule.

phi · Answer

notice what a great rule it is:
start with
$$ \frac{ 1}{x} $$
now use the idea that x to the 0 power is 1, so this is the same as
$$ \frac{x^0}{x^1} $$
use the subtract rule to get
$$  \frac{x^0}{x^1} = x^{0-1} = x^{-1}$$
that means
$$ \frac{ 1}{x} = x^{-1}$$