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Exponents Interesting Dilemma -

Hi Everyone,

Kind of new around here, but maybe someone can take a look at this and offer some advice.

I'm struggling with some exponents, anyone care to help?

-(-c^{4})^{-4}) = 1/c^{16 }however Maple 17 returns a different result -(-c^{4})^{-4}) = -1/c^{16 }

I have attached a PDF of a Maple page if anyone is interested to take a look and possibly point me in the right direction. Thanks in advance, I'm pretty sure I'm missing some concept regarding the negation and the parentheses, but not sure what it is.

Re: Exponents Interesting Dilemma -

Quote:

Originally Posted by

**cmmath** Hi Everyone,

Kind of new around here, but maybe someone can take a look at this and offer some advice.

I'm struggling with some exponents, anyone care to help?

-(-c^{4})^{-4}) = 1/c^{16 }however Maple 17 returns a different result -(-c^{4})^{-4}) = -1/c^{16 }

I have attached a PDF of a Maple page if anyone is interested to take a look and possibly point me in the right direction. Thanks in advance, I'm pretty sure I'm missing some concept regarding the negation and the parentheses, but not sure what it is.

To start with you need one less set of parenthesis:

$\displaystyle - \left ( c^4 \right ) ^{-4}$

Order of operations: Do exponents first.

$\displaystyle - \left ( c^4 \right ) ^{-4} = - c^{4 \times - 4} = \text{ ...}$

What happens to the - sign?

-Dan

Re: Exponents Interesting Dilemma -

Thanks

But would not the first set of parentheses remain? The exponent should become positive when it becomes 1/c^16?

Re: Exponents Interesting Dilemma -

Quote:

Originally Posted by

**cmmath** Thanks

But would not the first set of parentheses remain? The exponent should become positive when it becomes 1/c^16?

That's the problem here, and a common mistake. The negative sign out in front is not a part of the exponent. If you want to keep the extra parenthesis then

$\displaystyle \left ( - \left ( c^4 \right ) ^{-4} \right ) = \left ( - c^{-16} \right ) = \frac{-1}{c^{16}}$

-Dan

Re: Exponents Interesting Dilemma -

Thanks,

I see the issue, did you look at the PDF I attached to the original post. I'm still curious as to why Maple gives the different results?

Re: Exponents Interesting Dilemma -

Quote:

Originally Posted by

**cmmath** Thanks,

I see the issue, did you look at the PDF I attached to the original post. I'm still curious as to why Maple gives the different results?

Oh, okay. I see the problem. You have $\displaystyle (-c)^4$ When you raise a number to an even exponent, any negative signs are lost. So

$\displaystyle (-c)^4 \neq -c^4$

-Dan