Maths1210
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Hi I found this odd question in an exam paper and have never come across it before could You help me understand how to do it please?

Evaluate 16^(-3/2). (/ = fraction.)
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RDKGames
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(Original post by Maths1210)
Hi I found this odd question in an exam paper and have never come across it before could You help me understand how to do it please?

Evaluate 16^(-3/2). (/ = fraction.)
You need to be aware of the facts that a^{1/2}=\sqrt{a}, a^{-1}=\frac{1}{a}, and that (\sqrt{a})^n = \sqrt{a^n}

So simplify your problem by expressing it using fractions and roots.
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Maths1210
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(Original post by RDKGames)
You need to be aware of the facts that a^{1/2}=\sqrt{a}, a^{-1}=\frac{1}{a}, and that (\sqrt{a})^n = \sqrt{a^n}

So simplify your problem by expressing it using fractions and roots.
I do not really understand what I would be achieving by simplifying or
what that would do. Could you explain what I would be doing to evaluate it as I'm really confused by what it means by this in terms of maths?
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Einstein jnr.
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You have to change the 16^(-3/2) to 1/16^(3/2). Mathematically, 2^(-1) is same as 1/2^1.
So we can also write 1/16^(3/2) as 1/16^(3)x1/2. Anything to number 1/2 is the same as the square root of that number. So, 1/({√16}^3). The root of 16 is 4. Then we get 1/(4^3). And finally we get 1/64 or 64^-1 ( we have explained it in the second sentence of this writeup.
I hope you have gotten it.
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Sanjith Hegde123
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(Original post by Einstein jnr.)
You have to change the 16^(-3/2) to 1/16^(3/2). Mathematically, 2^(-1) is same as 1/2^1.
So we can also write 1/16^(3/2) as 1/16^(3)x1/2. Anything to number 1/2 is the same as the square root of that number. So, 1/({√16}^3). The root of 16 is 4. Then we get 1/(4^3). And finally we get 1/64 or 64^-1 ( we have explained it in the second sentence of this writeup.
I hope you have gotten it.
aw u spoiled it
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RDKGames
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(Original post by Maths1210)
I do not really understand what I would be achieving by simplifying or
what that would do. Could you explain what I would be doing to evaluate it as I'm really confused by what it means by this in terms of maths?
When it says 'evaluate' you can think of it as expressing a particular value in its simplest form.

For example, 4^{-1/2} is the same as \frac{1}{4^{1/2}} which is the same as \frac{1}{\sqrt{4}}, and the simplest way to express this is to say it is the same as  \frac{1}{2}, hence we'd say that 4^{-1/2} evaluates to \frac{1}{2} which is the simplest form.

This is what you need to do with your question.
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Maths1210
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(Original post by RDKGames)
When it says 'evaluate' you can think of it as expressing a particular value in its simplest form.

For example, 4^{-1/2} is the same as \frac{1}{4^{1/2}} which is the same as \frac{1}{\sqrt{4}}, and the simplest way to express this is to say it is the same as  \frac{1}{2}, hence we'd say that 4^{-1/2} evaluates to \frac{1}{2} which is the simplest form.

This is what you need to do with your question.
Why is 4^(-1/2) the same as root 4
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RDKGames
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(Original post by Maths1210)
Why is 4^(-1/2) the same as root 4
It's not. It's the same as 1/root(4)
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Maths1210
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(Original post by RDKGames)
It's not. It's the same as 1/root(4)
Is that not equal to 1/2?
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RDKGames
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(Original post by Maths1210)
Is that not equal to 1/2?
Yes. It's what I said when I was working it out.
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Maths1210
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(Original post by RDKGames)
Yes. It's what I said when I was working it out.
oh okay.
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Maths1210
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(Original post by Einstein jnr.)
You have to change the 16^(-3/2) to 1/16^(3/2). Mathematically, 2^(-1) is same as 1/2^1.
So we can also write 1/16^(3/2) as 1/16^(3)x1/2. Anything to number 1/2 is the same as the square root of that number. So, 1/({√16}^3). The root of 16 is 4. Then we get 1/(4^3). And finally we get 1/64 or 64^-1 ( we have explained it in the second sentence of this writeup.
I hope you have gotten it.
I'm not sure how you got to 64^(-1) from 1/4^(3).
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username3154862
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(Original post by Maths1210)
I'm not sure how you got to 64^(-1) from 1/4^(3).
4^-3/2

Ok, so deal with the negative first. You should know that negative power means 1/(number) eg. 2^-1 = 1/2

So it's 1/(4^3/2), thats the negative dealt with.
For the 4^3/2 bit. you convert that to a root and a power. The top one is the power, the bottom is the root.

So 4^3/2 -----> (sqrt(4^3)) = 64.
Ans = 1/64.



I'll give another example.
16^1/2 = sqrt(16^1)
16^1/3 = Cuberoot(16^1)
16^2/3 = Cuberoot(16^2)

Any questions, or if you're confused, just ask and I'll try explain better.
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username3154862
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(Original post by Maths1210)
I'm not sure how you got to 64^(-1) from 1/4^(3).
https://gyazo.com/0fd043d6628e89d5f4044e3e09652e9d here's a little extra to help, colour coordinated to make it easier to understand.
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