Question

the powers of 2 that are in the range 2  through 1,000 are 2,4,8,16,32,64,128,256,&512 .what does that  mean and it said find all the powers of 3 that are in range 3 through 1,000 

 

 

im so confused 

 

Answer 1

It means you need to find every power of 3 that are in the range of 3-1000 - the power is the number that says how many times you multiply the original number by itself
So 3 to the 1st power is 3 = 3
3 to the 2nd power is 3X3 = 9
3 to the 3rd power is 3X3X3 = 27
And so on... Hope I helped!

Answer 2

• the powers of 2 that are in the range 2 through 1,000 are 2,4,8,16,32,64,128,256,&512.

" This means that we are asked to find the value of
`2^n` for each n belonging to natural numbers.

Now we will stop our approximation when the value exceeds 1000.

i.e. the range is from 2-1000 ".

since the next number after 512 is 512×2=1024 which exceeds 1000. hence our successive approximation will stop at 512.

• similarly for the powers of 3 i.e.
  `3^n`

We will start writing our approximation and stop when it will exceed 1000.

i.e.
`3, 3^2=9,3^3=27,3^4=81,3^5=243,3^6=729`

i.e. the sequence is: 3,9,27,81,243,729.

We stopped at 729 because the next number in the series would be:

`3^7=2187`

which exceeds 1000.