#### Argile1845

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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.

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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.

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Use:

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.

(x

and simplify (ab^2) ^(-3)

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

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.

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.

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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?

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It should be (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?

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

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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?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^{-3}b^{-12}= 1/[a^{3}b^{12}] = 1/[3*2^{4}]=1/[3*16] = 1/48

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Ok, so [(a^3 * b^3)]^(-2) the first step is do is the inner parentheses- [(5*4)]^(-2) = (20)^(-2) =It should be (ab)^(-6)

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

Nevermind, I noticed my mistakeMat 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?

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CORRECT

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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?

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Things like that happen when you use a similar problem. A similar problem is different from the original one.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?

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You do realize you made a typo in your own problem, right?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= a

(ab^4) ^-3^{-3}b^{-12}= 1/[a^{3}b^{12}] = 1/[3*2^{4}]=1/[3*16] = 1/48

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

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So would this be [(a(^2 * ^-3) * b(^2 * ^-3)]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.

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?

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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?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?

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

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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.

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That would be 1/5*4*4= 1/80

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A and b are numbers and a^3=5 and b^3=4.

Find the value of (ab^2) ^-3

You mean 1/(5*4*4) = 1/80.That would be 1/5*4*4= 1/80

I think you've got it: \(\displaystyle (ab^2)^{-3}=a^{-3}b^{-6}=\frac{1}{a^3b^6}=\frac{1}{a^3(b^3)^2}=\frac{1}{5(4)^2}=\frac{1}{80}\)