Question

please help:) express the following in the form 2^n
2^70+2^70
answer: 2^71

Answer 1

if this was instead just: x + x

what would the answer be?

Answer 2

2x

Answer 3

correct, so now replace x by \(2^{70}\) and what do you get?

Answer 4

4^70...

Answer 5

not quite, you get two lots of \(2^{70}\) which can be written as:\[2\times2^{70}\]

Answer 6

you can now use the law of exponents to simplify this

Answer 7

e.g.:\[x^a\times x^b=x^{a+b}\]

Answer 8

use the fact that:\[2=2^1\]

Answer 9

ok i kinda get it

Answer 10

great! :)

Answer 11

its just confusing because i asumed that the answer would be 2^140

Answer 12

you have 2 to the power of 1 times 2 to the power of 70.
so, using the law of exponents I showed above, the answer should be 2 to the power of "1 plus 70"

Answer 13

think of a simpler example:\[2^3=2\times2\times2\]

Answer 14

so:\[2\times2^3=2\times2\times2\times2=2^4=2^{1+3}\]

Answer 15

first, this is a special case.. it is not a general rule
but 2^70 * 2^70 you add exponents to get 2^140

but here they are adding
2^70 + 2^70

you can factor out 2^70 to get 2^70(1+1) or 2^70 * 2^1 or 2^71

but notice this does NOT WORK:
2^70 + 2^70 + 2^70
you factor out 2^70 to get 2^70(1+1+1)= 3* 2^70 and that is all we can do

Answer 16

how would you do it with fractions though? like 2^1/3+2^1/3+2^1/3+2^1/3

Answer 17

same rules apply:\[2^a\times2^b=2^{a+b}\]even if a and b area fractions

Answer 18

you may find this helpful: http://www.mathsisfun.com/exponent.html

Answer 19

you could say
2^1/3+2^1/3+2^1/3+2^1/3
is the same as
4* 2^(1/3)
now it happens that 4 is 2^2 so you write it as
2^2 * 2^(1/3)
now use the add exponent rule : when multiplying two numbers with the SAME BASE, add their exponents

Answer 20

If you need more background, start with
http://www.khanacademy.org/math/algebra/exponents-radicals/v/understanding-exponents

it looks like there are quite a few videos, but they are short.

Answer 21

thanks alot :)