Laws of Exponents: Solve Math Homework Questions

[Meezus]

Hello, this isn't really a physics question but I'm getting pretty desperate and you guys have always been able to help me out before :)

1. Homework Statement
http://imgur.com/mYtJDLI

Homework Equations

I believe I'm suppose to use the Laws of Exponents.
For the first set possibly

but not sure as its addition in the question but can't find any laws with revolve around addition.

for the second set of questions I'm fairly certain its

once again but I'm just not 100% sure and I'm also not 100% sure what the question is actually asking.
[/B]

The Attempt at a Solution

3.2 + 0.007 = 3.27
10 x ^-4 + 10^-2 = 10^-6
3.27 x 10^-6

for the second set.
8²x 2^-3=
8²= 64
2^-3= 0.125
64 x 0.125 = 8
But now I'm not sure what to write, it asks for it as a power of 2? Does it just mean write 2³.

If anyone could help would be greatly appreciated.

 

[SteamKing]

Hello, this isn't really a physics question but I'm getting pretty desperate and you guys have always been able to help me out before :)

1. Homework Statement
http://imgur.com/mYtJDLI

Homework Equations

I believe I'm suppose to use the Laws of Exponents.
For the first set possibly

but not sure as its addition in the question but can't find any laws with revolve around addition.

for the second set of questions I'm fairly certain its

once again but I'm just not 100% sure and I'm also not 100% sure what the question is actually asking.
[/B]

The Attempt at a Solution

3.2 + 0.007 = 3.27
10 x ^-4 + 10^-2 = 10^-6
3.27 x 10^-6

for the second set.
8²x 2^-3=

I don't think the problem wants you to convert 8² and 2^-3 to decimals, but instead express each number as a power of 2.

Expressing 2^-3 as a power of 2 is easy.

Can you express 8 as a power of 2?

If you can, then what would 8² be expressed as a power of 2?

Once you do this, then what is the product of 8² and 2^-3, evaluated using the laws of exponents?

 

[SammyS]

Hello, this isn't really a physics question but I'm getting pretty desperate and you guys have always been able to help me out before :)

1. Homework Statement
http://imgur.com/mYtJDLI

Homework Equations

I believe I'm suppose to use the Laws of Exponents.
For the first set possibly

but not sure as its addition in the question but can't find any laws with revolve around addition.

for the second set of questions I'm fairly certain its

once again but I'm just not 100% sure and I'm also not 100% sure what the question is actually asking.
[/B]

The Attempt at a Solution

3.2 + 0.007 = 3.27
10 x ^-4 + 10^-2 = 10^-6
3.27 x 10^-6

That's incorrect. If you check it with a calculator you'll see that.

For sure, 10 x ^-4 + 10^-2 is 1/10000 + 1/100. That definitely is not 1/1000000 .

You are to add:

3.2×10^-4 + 0.07×10^-2​

This similar to adding "like" terms, but those terms are not alike.

Rewrite one or both of them.

For instance, 0.07 = 7×10^-2, so 0.07×10^-2 = 7×10^-2×10^-2=7×10^-4. Right?

Now both terms are alike, so you can add coefficients.

for the second set.
8²x 2^-3=
8²= 64
2^-3= 0.125
64 x 0.125 = 8
But now I'm not sure what to write, it asks for it as a power of 2? Does it just mean write 2³.

If anyone could help would be greatly appreciated.

 

[haruspex]

3.2 + 0.007 = 3.27
10 x -4 + 10-2 = 10-6
3.27 x 10-6

That is completely wrong, I'm sorry to say.
What is 3.2 x 10^-4 as a decimal number?

 

[Meezus]

I don't think the problem wants you to convert 8² and 2^-3 to decimals, but instead express each number as a power of 2.

Expressing 2^-3 as a power of 2 is easy.

Can you express 8 as a power of 2?

If you can, then what would 8² be expressed as a power of 2?

Once you do this, then what is the product of 8² and 2^-3, evaluated using the laws of exponents?

I don't think the problem wants you to convert 8² and 2^-3 to decimals, but instead express each number as a power of 2.

Expressing 2^-3 as a power of 2 is easy.

Can you express 8 as a power of 2?

If you can, then what would 8² be expressed as a power of 2?

Once you do this, then what is the product of 8² and 2^-3, evaluated using the laws of exponents?

Would 8² be 2⁶?
so the answer would be?
2⁶ x 2^-3 = 2⁶+^-3

 

[Meezus]

That is completely wrong, I'm sorry to say.
What is 3.2 x 10^-4 as a decimal number?

0.00032 but people in another thread are telling me not to convert into decimals?

 

[SammyS]

0.00032 but people in another thread are telling me not to convert into decimals?

Don't post the same thread in more than one place !
Mod note: I merged the two threads into a single thread here.

 

[haruspex]

0.00032 but people in another thread are telling me not to convert into decimals?

For this problem you must do some conversion to decimals, though there is a slightly neater way than I'm suggesting you use. Let's get you to the point of finding the right answer first, then we can revisit that.
Please post a link to the other thread.

 

[Meezus]

For this problem you must do some conversion to decimals, though there is a slightly neater way than I'm suggesting you use. Let's get you to the point of finding the right answer first, then we can revisit that.
Please post a link to the other thread.

Ok thanks :)

 

[Meezus]

Don't post the same thread in more than one place !

Yeah sorry wasn't 100% sure where to post it, so it posted in two places

 

[haruspex]

Ok thanks :)

The advice not to convert to decimals was for the second question. For addition and subtraction you do, for multiplication and division you don't.

 

[haruspex]

Yeah sorry wasn't 100% sure where to post it, so it posted in two places

It clearly belongs in precalc math, it is not a physics question.
Mod note: Merged the two threads into the one here in precalc.
If you feel it necessary to post on two forums (but it never should be) at least post one thread as a link to the other so that all the responses go on the same thread.

 

[Meezus]

The advice not to convert to decimals was for the second question. For addition and subtraction you do, for multiplication and division you don't.

Oh yes, sorry.

For the first one is it:
3.2 x 10^-4 = 0.00032
0.07 x 10^-2 = 0.0007
0.00032 + 0.0007 = 0.00102?

 

[haruspex]

Oh yes, sorry.

For the first one is it:
3.2 x 10^-4 = 0.00032
0.07 x 10^-2 = 0.0007
0.00032 + 0.0007 = 0.00102?

Yes.
The neater method I mentioned I see has already been described to you by SammyS in the other thread. It consists of extracting a power of 10 as a common factor. This makes the expansion to decimals a bit easier.

 

[SteamKing]

Would 8² be 2⁶?
so the answer would be?
2⁶ x 2^-3 = 2⁶+^-3

Which is?

 

[Meezus]

Which is?

2³?

 

[SteamKing]

Correct.

 

[Meezus]

Yes.
The neater method I mentioned I see has already been described to you by SammyS in the other thread. It consists of extracting a power of 10 as a common factor. This makes the expansion to decimals a bit easier.

The question does state to show how I manipulated the powers of 10, would it be possible for you to explain this other method as I don't really understand the other explanation.

Thank you for you help so far :)

 

[haruspex]

The question does state to show how I manipulated the powers of 10, would it be possible for you to explain this other method as I don't really understand the other explanation.

Thank you for you help so far :)

I'll make it general and see if you can figure out how to apply it to the question.
Suppose you have a.n^b+c.n^d. Note that the bases of both exponentiated factors are n.
This allows you to take out a common factor of the form n^k, for any k you choose.
a.n^b=a.n^b-k.n^k (use the law of exponents you quoted to check this).
a.n^b+c.n^d=a.n^b-k.n^k+c.n^d-k.n^k=(a.n^b-k+c.n^d-k).n^k.
We choose k=d:
(a.n^b-d+c).n^d.
Now all you have to do is write out a.n^b-d as a decimal and add c to it.

 

[Meezus]

That's incorrect. If you check it with a calculator you'll see that.

For sure, 10 x ^-4 + 10^-2 is 1/10000 + 1/100. That definitely is not 1/1000000 .

You are to add:

3.2×10^-4 + 0.07×10^-2​

This similar to adding "like" terms, but those terms are not alike.

Rewrite one or both of them.

For instance, 0.07 = 7×10^-2, so 0.07×10^-2 = 7×10^-2×10^-2=7×10^-4. Right?

Now both terms are alike, so you can add coefficients.

Sorry for replying so late, this took me a while to understand. Is this correct:
3.2 = 32000 x 10^-4
10^-4 + 10^-4 = 10^-8

0.07 = 7 x 10^-2
10^-2 + 10^-2 = 10^-4

32000 x 10^-8 + 7 x 10^-4

 

[NascentOxygen]

Sorry for replying so late, this took me a while to understand. Is this correct:
3.2 = 32000 x 10^-4
10^-4 + 10^-4 = 10^-8

0.07 = 7 x 10^-2
10^-2 + 10^-2 = 10^-4

32000 x 10^-8 + 7 x 10^-4

Each of these can be checked on your calculator. You'll find one or two are wrong, and this will lead on to finding where you went astray, and why. Use your calculator to evaluate the side of the equation which contains a "+" or "x" sign, and see whether it comes out as equal to the number on the other side of the equation.

 

[SammyS]

Sorry for replying so late, this took me a while to understand. Is this correct:
3.2 = 32000 x 10^-4
10^-4 + 10^-4 = 10^-8

0.07 = 7 x 10^-2
10^-2 + 10^-2 = 10^-4

32000 x 10^-8 + 7 x 10^-4

No to all most of that.

As you might imagine, 10^-4 + 10^-4 = 2×10^-4

and 10^-2 + 10^-2 = 2×10^-2

 

[haruspex]

Sorry for replying so late, this took me a while to understand. Is this correct:
3.2 = 32000 x 10^-4
10^-4 + 10^-4 = 10^-8

0.07 = 7 x 10^-2
10^-2 + 10^-2 = 10^-4

32000 x 10^-8 + 7 x 10^-4

Maybe it will help you if we make this more concrete.
One millimetre is one thousandth of a metre. We can write one thousandth as 10^-3. What's one millimetre plus one millimetre? That would be 10^-3+10^-3 metres = ... what?