Question

Can't use a calculator

Answer 1

\[\frac{2 ^{30} -2^{29}}{ 2 }\]

Answer 2

Can I reduce it? Like 2^4-2^3 / 2 and it turn out the same?

Answer 3

Factor out 2^29 from the numerator.

Answer 4

Hum. Can you show me how to do that with the exp? I understand factoring but I'm afraid I will kill it.

Answer 5

Example: \(x^{30} - x^{29} = x^{29}(x - 1)\)

Now replace x with 2.

Answer 6

if you have android download the app called wabbitemu it will give you a texas instraments calcator

Answer 7

Suppose you have `n` apples.
If you throw away half of them, how many apples you will be left with ?

Answer 8

*Without a calculator*

Ok @mathstudent55

\[\frac{ 2^{29}(x-1) }{ 2 }\]

Answer 9

Replace x with 2 in the parentheses also.

Answer 10

Oh yea my bad

Answer 11

\[\frac{ 2^{29}(2-1) }{ 2 }\]

Answer 12

Now what is 2 - 1? It's just numbers, so you can do the subtraction.

Answer 13

1

Answer 14

So just 2^29 on top

Answer 15

Right, so you have

\(\dfrac{2^{29}}{2^1} \)

How do you divide powers with the same base?

Answer 16

Subtract, right?

Answer 17

Correct.

Answer 18

So I am at
\[2^{28}\]

Answer 19

That is correct.

Answer 20

Ok. Well, thankfully I can stop there...it does not want an actual number value. Thanks!

Answer 21

Now just give me a minute.
Look above at what @ganeshie8 wrote.

Answer 22

Notice that when you have powers of 2, each next higher integer power is 2 times the previous power.
This is what I mean.

For example,
\(2^{30} = 2^{29} \times 2\)

\(2^{15} = 2^{14} \times 2\)

In general,

\(2^{n + 1} = 2^n \times 2\)

Ok so far?

Answer 23

Yes, I follow.

Answer 24

And thanks for taking so much time to explain this BTW.

Answer 25

That means each power of 2 is half of the next higher integer power of 2.

In general

\(2^n = \dfrac{2^{n + 1}}{2} \)

That means, for the powers used in this problem,

\(2^{29} = \dfrac{2^{30}}{2} \)

Answer 26

Wow thanks so much!

Answer 27

That means in the numerator of the fraction, where you have \(2^{30} - 2^{29}\), you are subtracting half of \(2^{30}\).

Then you can conclude immediately that \(2^{30} - 2^{29} = 2^{29} \)

Answer 28

Then when you divide \(2^{29}\) by 2, as the denominator of the fraction shows, you get \(2^{28} \)

Answer 29

This second approach is all based on what @ganeshie8 asked above.

Answer 30

You're welcome.