3nth sqrt (x-9)^3

- anonymous

3nth sqrt (x-9)^3

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- anonymous

\[(\sqrt[3]{x-9})^3\]
If you cube a cubed root you just remove them both.
\[\sqrt[3]{a^3} = \sqrt[3]{a}^3 = a^{\frac{3}{3}} = a^1 = a \]

- anonymous

its whats inside the radical thats confusing me

- anonymous

x - 9 is just x - 9

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## More answers

- anonymous

Or do I misunderstand your question?

- anonymous

well. i have another problem thats like that and i just dont know what to do with (x-anything)^anything

- anonymous

Just expand it and simplify as much as possible. Unless you have an equal there you can't really solve for x.

- anonymous

so you foil within the radical to expand it?

- anonymous

Well if it's something cubed inside a cubed root, there's no need to foil it cause the two cancel eachother out. Otherwise yeah you'd have to distribute (foil) and hope it turns out nicely.

- anonymous

so the answer is just x-9

- anonymous

Yep.

- anonymous

Assuming that it is as I have it written originally.

- anonymous

thank you, can you help me with sqrt 25(x+2)^4

- anonymous

Of course.

- anonymous

Can you quickly rewrite each of those factors as a square?

- anonymous

25 is what squared?

- anonymous

5

- anonymous

And \((x+2)^4 \) is what squared?

- anonymous

that i dont know

- anonymous

Oh. well what if I asked you what \((2^2)^2\) was. Do you know that?

- anonymous

wouldnt that be 16?

- anonymous

Yes, but don't think about it that way ;p

- anonymous

Think about it as \(2^4\)

- anonymous

When you raise a power to a power you multiply the exponents

- anonymous

Have you been taught this?

- anonymous

the teacher i have sucks. so probably have but not the way your explaining it

- anonymous

Hrm. Ok, well so if raising something to a power multiplies exponents, then taking the root of a power divides the exponent.

- anonymous

For example.
\[\sqrt{5^4} = 5^2\]
\[\sqrt[3]{7^{12}} = 7^4\]
etc.

- anonymous

So if you have
\[\sqrt{a^4} =\ ?\]

- anonymous

okaie. so would (x+2)^4 would just be x+2 ^ 2. and the answer to your question is a^2

- anonymous

Yes precisely. So for your problem you had
\[\sqrt{5^2(x+2)^4} =\ ?\]

- anonymous

well it was 25 which = 5^2.

- anonymous

Right. Same difference, so take the square root of that and you get?

- anonymous

5(x+2)^2

- anonymous

Exactly.

- anonymous

THANKK YOU SO MUCH

- anonymous

Very welcome ! =)

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