A and b are numbers

Argile1845

New member
Joined
Feb 19, 2021
Messages
32
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

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
24,713
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

Elite Member
Joined
Nov 12, 2017
Messages
11,540
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

New member
Joined
Feb 19, 2021
Messages
32
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

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
24,713
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

Elite Member
Joined
Dec 30, 2014
Messages
10,589
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

New member
Joined
Feb 19, 2021
Messages
32
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

New member
Joined
Feb 19, 2021
Messages
32
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
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
24,713

Argile1845

New member
Joined
Feb 19, 2021
Messages
32
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

New member
Joined
Feb 19, 2021
Messages
32
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

Elite Member
Joined
Dec 30, 2014
Messages
10,589
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

Elite Member
Joined
Nov 12, 2017
Messages
11,540
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

New member
Joined
Feb 19, 2021
Messages
32
That's what I thought and is what I was asking.
 

Argile1845

New member
Joined
Feb 19, 2021
Messages
32
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

Elite Member
Joined
Nov 12, 2017
Messages
11,540
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

New member
Joined
Feb 19, 2021
Messages
32
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

New member
Joined
Feb 19, 2021
Messages
32
That would be 1/5*4*4= 1/80
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
11,540
Top