Solving Math Problem: Express -2^4 + 3^-1

[Cornraker]

Homework Statement

Express the number in the form a/b

Homework Equations

$$-2^{4} + 3^{-1}$$

The Attempt at a Solution

16+(-3) = 13

Why is this not the correct answer?

 

[sara_87]

1) should the negative sign in the term -2^4 be inside the bracket? should it be (-2)^4? If yes then 16 is correct.

2) for any number, say x, x^(-1)=1/x not -x.

can you do it now?

 

[Cornraker]

Well if the negative sign is outside as such: -(2^4), does that make it a -16 instead of positive?

 

[sara_87]

yes.

so what do you get for the answer?

 

[Mark44]

Well if the negative sign is outside as such: -(2^4), does that make it a -16 instead of positive?

Yes, as opposed to (-2)⁴, which is 16.

Both what you have written, -(2⁴), and -2⁴ are equal to -16.

 

[Cornraker]

47/3.

After you told me 3^-1 was not -3 but instead 1/3, i was able to figure it out. I cross multiplied -16 with 1/3 and i came out with 48 then when i added the fraction i came out with 47/3. does it sound right?

 

[sara_87]

you cross multiplied??

you just have to add -16 to 1/3.

I think you have the answer...you just forgot a minus sign...right? ;)

 

[Cornraker]

This problem is giving me trouble. The correct answer is 47/3. I just can't figure out how to arrive at it. I thought i could arrive by cross multiplying, but looking at it again, it doesn't seem right.

 

[Mark44]

This problem is giving me trouble. The correct answer is 47/3. I just can't figure out how to arrive at it. I thought i could arrive by cross multiplying, but looking at it again, it doesn't seem right.

Are you sure you have given us the problem verbatim? The answer to the problem you posted is -47/3, not 47/3.

-2⁴ + 3^-1 = -16 + 1/3 = -48/3 + 1/3 = -47/3

To get a common denominator of 3, you multiply -16 by 1 (in the form of 3/3) to get -48/3. Now both denominators are 3 and you can add the numerators.

 

[Cornraker]

Are you sure you have given us the problem verbatim? The answer to the problem you posted is -47/3, not 47/3.

Yes sorry i meant to say -47/3. I wasnt sure how you arrived at -48/3 but i realize i forgot about finding the common denominator