Simplification and solving of equation

[chikis]

Homework Statement

The problem are two:
(1) Simplify: 1/4(2ⁿ- 2ⁿ⁺²)

(2) Solve the equation 2^(2x+1)- 9(2^x) + 4 = 0

Homework Equations

The Attempt at a Solution

for the number one question, simplify:
1/4(2ⁿ- 2ⁿ⁺²)

1/4(2ⁿ- 2ⁿ⁺²)
= 4^-1(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ*2²
I can't go further please I need asistance.

For the second question, solve the equation:
2^(2x+1)- 9(2^x) + 4 = 0

I don't just know how to start dealing with the question. It is really a troubsome question.

 

[Villyer]

I'm confused as to your original equations.

$$(1)\frac{1}{4}2^n-2^{n+2}$$
$$(2)\ 2^{2x+1} - 9(2^x + 4)$$

Are those correct?

 

[Ray Vickson]

Homework Statement

The problem are two:
(1) Simplify: 1/4(2n[sup/]- 2n+2[sup/])

(2) Solve the equation 2(2x+1)- 9(2x[sup/] + 4 = 0

Homework Equations

The Attempt at a Solution

for the number one question, simplify:
1/4(2<sup>n[sup/]- 2n+2[sup/])

1/4(2n[sup/]- 2n+2[sup/])
= 4-1[sup/](2n[sup/]-2n+2[sup/])
= 2(-2)[sup/](2n[sup/]-2n+2[sup/])
= 2(-2)[sup/](2n[sup/]-2n[sup/]*22[sup/]
I can't go further please I need asistance.

For the second question, solve the equation:
2(2x+1)- 9(2x[sup/] + 4 = 0
I don't just know how to start dealing with the question. It is really a troubsome question.</sup>

<sup>Use [S U P] and [/S U P] (but with no spaces), not [sup ] and [ /sup]. In fact, just use the "X2" button on the palette at the top in the input panel.

RGV</sup>

 

[chikis]

Use [S U P] and [/S U P] (but with no spaces), not [sup ] and [ /sup]. In fact, just use the "X²" button on the palette at the top in the input panel.

RGV

I have edited the problem so that it can be seen clearly.

 

[chikis]

I'm confused as to your original equations.

$$(1)\frac{1}{4}2^n-2^{n+2}$$
$$(2)\ 2^{2x+1} - 9(2^x + 4)$$

Are those correct?

I have edited my opening post so that it can be seen clearly. Maybe you can look at the problem again.

 

[Villyer]

For (1), you are close. Combine like terms.

For (2), it is actually a quadratic. Can you see what the variable is?

 

[chikis]

For (1), you are close. Combine like terms.

If like terms is collected, the expression will look like this:
2^(-2)*2²(2ⁿ-2ⁿ)
= 2(2ⁿ-2ⁿ)
= 2ⁿ⁺¹-2ⁿ

For (2), it is actually a quadratic. Can you see what the variable is?

No! I didn't see the variable.

 

[Mentallic]

If like terms is collected, the expression will look like this:
2^(-2)*2²(2ⁿ-2ⁿ)

This does not follow from the last line you had written in your opening post:

= 2^(-2)(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ*2²

What we have so far is

$$2^{-2}(2^n-2^n\cdot 2^2)$$

Can you expand this?

No! I didn't see the variable.

There is a basic rule of exponentiation that says that if you exponentiate an exponent, you multiply the exponents together. What this is saying is that
$$(a^m)^n=a^{mn}$$

So then what does $(2^x)^2$ simplify to?

 

[eumyang]

If like terms is collected, the expression will look like this:
2^(-2)*2²(2ⁿ-2ⁿ)
= 2(2ⁿ-2ⁿ)
= 2ⁿ⁺¹-2ⁿ

Nope. Look at the last step in your original post:

1/4(2ⁿ- 2ⁿ⁺²)

1/4(2ⁿ- 2ⁿ⁺²)
= 4^-1(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ*2²)

Answer this: what is x - 4x?
Now answer this: what is 2ⁿ - 4*2ⁿ?
That's what Villyer meant by combining terms.

No! I didn't see the variable.

$2^{2x+1} - 9\cdot 2^x + 4$
Rewrite the 1st term so it looks like (something) times 2^2x.EDIT: Beaten to it.

 

[chikis]

I don't understand what you guys are writing, write using the same format I used in showing my raise to power in my opening post. I will understand it better and therefore be able to respond to the numerous replies you guys are posting.

 

[Mentallic]

I don't understand what you guys are writing, write using the same format I used in showing my raise to power in my opening post. I will understand it better and therefore be able to respond to the numerous replies you guys are posting.

You can't see Latex? I think you should try find out and fix what the problem is on your end, because Latex is commonly used on this forum and not just in this thread.

 

[chikis]

You can't see Latex? I think you should try find out and fix what the problem is on your end, because Latex is commonly used on this forum and not just in this thread.

Please help me, I believe I would be able to understand and write using latex with time. Please help me, I really need this help please!

 

[Mentallic]

Please help me, I believe I would be able to understand and write using latex with time. Please help me, I really need this help please!

I'm not asking you to learn to use latex so suddenly, but rather I'm confused as to why you can't read what we've written. Correct me if I'm wrong, but I think that Latex is software that's inbuilt into this forum, so basically everyone can read it (unless they have some horribly outdated internet browser).

Anyway, I'll edit what emuyang and I wrote in the format you've requested.

This does not follow from the last line you had written in your opening post:What we have so far is

2^-2*(2ⁿ - 2ⁿ*2²)

Can you expand this?There is a basic rule of exponentiation that says that if you exponentiate an exponent, you multiply the exponents together. What this is saying is that
(a^m)ⁿ=a^mn

So then what does (2^x)² simplify to?

Nope. Look at the last step in your original post:

Answer this: what is x - 4x?
Now answer this: what is 2ⁿ - 4*2ⁿ?
That's what Villyer meant by combining terms.2^2x+1 - 9*2^x + 4
Rewrite the 1st term so it looks like (something) times 2^2x.EDIT: Beaten to it.

EDIT: Changed the ^ to [sup ] tags

 

[Ray Vickson]

Please help me, I believe I would be able to understand and write using latex with time. Please help me, I really need this help please!

You have been given lots of help---any more help and we would be doing your homework for you. If you are having trouble understanding what people write you need to sit down with a pencil and several sheets of paper and start writing things down in whatever notation you like.

RGV

 

[chikis]

You have been given lots of help---any more help and we would be doing your homework for you. If you are having trouble understanding what people write you need to sit down with a pencil and several sheets of paper and start writing things down in whatever notation you like.

RGV

I did not ask you to do my home work. What I ask is this: give me directions that will help me do the homework. That's all that I ask, anything far from that then you are doing my homework. I know that you are giving me some asistance, but how can I work with the language I don't understand. I know that apart from latex, there are other formats that can be used and I will be able to understand all the replies you are posting and be able to respond accordingly.

 

[Ray Vickson]

I did not ask you to do my home work. What I ask is this: give me directions that will help me do the homework. That's all that I ask, anything far from that then you are doing my homework. I know that you are giving me some asistance, but how can I work with the language I don't understand. I know that apart from latex, there are other formats that can be used and I will be able to understand all the replies you are posting and be able to respond accordingly.

Here is what one responder said to you:

"Answer this: what is x - 4x?
Now answer this: what is 2ⁿ - 4*2ⁿ? "

So, what are your answers? Do you see why the answers are important?

RGV

 

[chikis]

Here is what one responder said to you:

"Answer this: what is x - 4x?

Is just an expression an algebraic expression. If factored it will look like this: x(1-4)
= x(1-2)(2+1)

Now answer this: what is 2ⁿ - 4*2ⁿ? "

So, what are your answers? Do you see why the answers are important?

RGV

That is 2 raise power n minus 4 times 2 raise to power n. It can be simplified further to appear like this: 2ⁿ - 2² * 2ⁿ
= 2ⁿ/2²⁺ⁿ
= 2^n-(2+n)
= 2^n-2-n

 

[Mark44]

Is just an expression an algebraic expression. If factored it will look like this: x(1-4)
= x(1-2)(2+1)

But neither of these is the simplest way to write it. It's not very useful to factor 1 - 4.

That is 2 raise power n minus 4 times 2 raise to power n. It can be simplified further to appear like this: 2ⁿ - 2² * 2ⁿ

The above is not wrong, but it's not helpful to write 4 as 2².
Your work below here is incorrect.

= 2ⁿ/2²⁺ⁿ
= 2^n-(2+n)
= 2^n-2-n

These two problems are similar, and you are making them much more complicated than they deserve.

 

[chikis]

But neither of these is the simplest way to write it. It's not very useful to factor 1 - 4.
The above is not wrong, but it's not helpful to write 4 as 2².
Your work below here is incorrect.


These two problems are similar, and you are making them much more complicated than they deserve.

What else can I do then?

 

[SammyS]

What else can I do then?

1 - 4 = -3, Correct ?

 

[chikis]

1 - 4 = -3, Correct ?

Oh no! You just reminded me that x-4x is also -3x. Anyway thanks for that. The question is what else can I do?

 

[Mark44]

So now what is 2ⁿ - 4*2ⁿ in its simplest form?

 

[chikis]

So now what is 2ⁿ - 4*2ⁿ in its simplest form?

It can be expressed as: 2ⁿ-2²*2ⁿ
= 2ⁿ-2²*2ⁿ
= 2ⁿ/2²⁺ⁿ
= 2^n-2-n
= 2²
= 4

 

[Mark44]

It can be expressed as: 2ⁿ-2²*2ⁿ
= 2ⁿ-2²*2ⁿ
= 2ⁿ/2²⁺ⁿ

No, there's no property of exponents that let's you do this (above).

= 2^n-2-n
= 2²
= 4

Start with this: 2ⁿ-2²*2ⁿ, and factor out 2ⁿ.

 

[chikis]

No, there's no property of exponents that let's you do this (above).


Start with this: 2ⁿ-2²*2ⁿ, and factor out 2ⁿ.

what I can make out from: 2ⁿ-2²*2ⁿ
Is that 2 is common here, but how to factorise 2ⁿ out, I don't know because am not use to that kind of factorisation where the whole terms is raised to a power, different powers for that matter.

 

[SammyS]

what I can make out from: 2ⁿ-2²*2ⁿ
Is that 2 is common here, but how to factorise 2ⁿ out, I don't know because am not use to that kind of factorisation where the whole terms is raised to a power, different powers for that matter.

2ⁿ is in common .

Let x = 2ⁿ. then you have x - (2²)*x .

What does that simplify to?

 

[chikis]

2ⁿ is in common .

Let x = 2ⁿ. then you have x - (2²)*x .

What does that simplify to?

How can 2ⁿ be common, when the whole three terms are raised different powers? What about the other 2 that is raised to power two?
If x = 2ⁿ
----> x - (2²)*x .

= x - 4x
= -3x

 

[SammyS]

...

If x = 2ⁿ
----> x - (2²)*x .

= x - 4x
= -3x

Right.

And if x = 2ⁿ , that gives you

-3x → (-3) (2ⁿ).​

 

[gabbagabbahey]

How can 2ⁿ be common, when the whole three terms are raised different powers? What about the other 2 that is raised to power two?

This is a simple application of a basic property of multiplication, called the distributive property. Surely you must be familiar with this property, right?

A(B+C)=A*B+A*C

Applying this property with A=2ⁿ B=1 and C=-2², and recognizing that 2ⁿ=2ⁿ*1, gives you 2ⁿ-2²*2ⁿ=2ⁿ(1-2²). This is what is meant by "factoring out" 2ⁿ.

 

[Ray Vickson]

How can 2ⁿ be common, when the whole three terms are raised different powers? What about the other 2 that is raised to power two?
If x = 2ⁿ
----> x - (2²)*x .

= x - 4x
= -3x

Congratulations. You managed too have others complete your homework for you. Well done.

RGV

 

[Mentallic]

Congratulations. You managed too have others complete your homework for you. Well done.

RGV

Give the guy a break, he's been struggling with applying a simple factorization. Dragging him along for days to answer such a brief question is probably not the best approach here.
He's also taken multiple attempts at the answer thus far.

 

[Ray Vickson]

Give the guy a break, he's been struggling with applying a simple factorization. Dragging him along for days to answer such a brief question is probably not the best approach here.
He's also taken multiple attempts at the answer thus far.

I genuinely believe that the best way for him to learn is to get a mark of zero on that problem and to then study the posted solutions after getting his paper back. That way he might actually, finally, absorb and *understand* the material.

RGV

 

[chikis]

Congratulations. You managed too have others complete your homework for you. Well done.

RGV

Nothing has been completed yet because I cannot work with what I don't understand. So the thread is still going on.

 

[chikis]

Give the guy a break, he's been struggling with applying a simple factorization. Dragging him along for days to answer such a brief question is probably not the best approach here.
He's also taken multiple attempts at the answer thus far.

Nothing has been completed yet because I cannot work with what I don't understand. So the thread is still going on.

 

[chikis]

I genuinely believe that the best way for him to learn is to get a mark of zero on that problem and to then study the posted solutions after getting his paper back. That way he might actually, finally, absorb and *understand* the material.

RGV

You want me to fail? Then you are not helping matters.