A and b are numbers

Argile1845

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A and b are numbers and a^3=5 and b^3=4.
Find the value of (ab^2) ^-3

I need help starting this. This one is stumping me but I know it's simple I'm just looking at it all wrong.
 

Subhotosh Khan

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A and b are numbers and a^3=5 and b^3=4.
Find the value of (ab^2) ^-3

I need help starting this. This one is stumping me but I know it's simple I'm just looking at it all wrong.
Use:

(xn)m = x(n*m)

and simplify (ab^2) ^(-3)
 

Dr.Peterson

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A and b are numbers and a^3=5 and b^3=4.
Find the value of (ab^2) ^-3

I need help starting this. This one is stumping me but I know it's simple I'm just looking at it all wrong.
You can first apply the fact that (xy)^n = x^n y^n.

Then you can apply the fact that (x^m)^n = x^(mn).

Are you familiar with these?

There will be more to do, but that is a start.

Give it a try and show some work, so we see where you stand.
 

Argile1845

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Well so far I have ab^-6
I know that a^3=5 and b^3=4 so if I split the ^-6 up I'd have -5*-5*-4*-4=400?
 

Subhotosh Khan

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Well so far I have ab^-6
I know that a^3=5 and b^3=4 so if I split the ^-6 up I'd have -5*-5*-4*-4=400?
It should be (ab)^(-6)

(ab)^(-6) = [(a * b)^(3)]^(-2) = [(a^3 * b^3)]^(-2) ....... continue
 

Jomo

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I'll do a similar one for you.
a and b are numbers and a^3=3 and b^3=2.
Find the value of (ab^3) ^-3

(ab^4) ^-3 = a-3b-12 = 1/[a3b12] = 1/[3*24]=1/[3*16] = 1/48
 

Argile1845

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I'll do a similar one for you.
a and b are numbers and a^3=3 and b^3=2.
Find the value of (ab^3) ^-3

(ab^4) ^-3 = a-3b-12 = 1/[a3b12] = 1/[3*24]=1/[3*16] = 1/48
Mat I ask why you changed the sign in the step from (ab^3)^-3 to (ab^4) ^-3? Why did the exponent change to a 4th power when it was a 3 to begin with?
 

Argile1845

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It should be (ab)^(-6)

(ab)^(-6) = [(a * b)^(3)]^(-2) = [(a^3 * b^3)]^(-2) ....... continue
Ok, so [(a^3 * b^3)]^(-2) the first step is do is the inner parentheses- [(5*4)]^(-2) = (20)^(-2) =
Mat I ask why you changed the sign in the step from (ab^3)^-3 to (ab^4) ^-3? Why did the exponent change to a 4th power when it was a 3 to begin with?
Nevermind, I noticed my mistake
 

Argile1845

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Aaahhh, do you know how happy that makes me?! Whew. Thank you so much. Learning on my own and it's so difficult. Thanks again! Sorry for ally questions but I have no one else.
 

Argile1845

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I'm just concerned about one thing...
On the original question it had (ab^2)^-3... But in the question above that I solved I was multiplying the a and the b by the ^3power before multiplying it by a ^ -2 power.. Can I really switch those places?
 

Jomo

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Mat I ask why you changed the sign in the step from (ab^3)^-3 to (ab^4) ^-3? Why did the exponent change to a 4th power when it was a 3 to begin with?
Things like that happen when you use a similar problem. A similar problem is different from the original one.
 

Dr.Peterson

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I'll do a similar one for you.
a and b are numbers and a^3=3 and b^3=2.
Find the value of (ab^3) ^-3

(ab^4) ^-3
= a-3b-12 = 1/[a3b12] = 1/[3*24]=1/[3*16] = 1/48
You do realize you made a typo in your own problem, right?
 

Argile1845

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That's what I thought and is what I was asking.
 

Argile1845

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You can first apply the fact that (xy)^n = x^n y^n.

Then you can apply the fact that (x^m)^n = x^(mn).

Are you familiar with these?

There will be more to do, but that is a start.

Give it a try and show some work, so we see where you stand.
So would this be [(a(^2 * ^-3) * b(^2 * ^-3)]
Which would equal (a^-6 * b^-6) correct?
I know a^3=5 so I want to simplify this and say (-5*-5*-4*-4) = 400... I still get 400.
What am I doing wrong?
 

Dr.Peterson

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So would this be [(a(^2 * ^-3) * b(^2 * ^-3)]
Which would equal (a^-6 * b^-6) correct?
I know a^3=5 so I want to simplify this and say (-5*-5*-4*-4) = 400... I still get 400.
What am I doing wrong?
What you wrote there is meaningless; I suppose you meant a^(2*-3) b^(2*-3). But if you started with (ab^2)^-3 from your problem, that is wrong. Do you see where?

Also, if a^3 = 5, then a^-6 is not -5*-5. In fact, a^-3 is not -5. Negative exponents don't change the sign of the result; they product a reciprocal: a^-n = 1/a^n, not -a^n. That is probably a big part of your difficulty.
 

Argile1845

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This helps a lot, thank you. I realize that now, how did I forget that?!
I am sorry about the typing. I am new at having to type it out and I can get mess it up. Thank you for being patient with me.
 

Argile1845

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That would be 1/5*4*4= 1/80
 

Dr.Peterson

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