# Laws of Exponents

• Jun 2nd 2011, 04:03 PM
Chevytuff19
Laws of Exponents
Hello,

First, I just want to say "Hello!" since I am new here. I am just starting my PreCal class this summer. I am a CS major, but have to take it for my degree.

My problem is this:

I have to express the following as a number in the form a/b, assuming a and b are integers.

-2^4 + 3^-1

I know that to get rid of the negative exponent I need to make it 1/3^1. However, I cannot seem to figure it out completely. Any help would be appreciated.
• Jun 2nd 2011, 04:10 PM
TheEmptySet
Quote:

Originally Posted by Chevytuff19
Hello,

First, I just want to say "Hello!" since I am new here. I am just starting my PreCal class this summer. I am a CS major, but have to take it for my degree.

My problem is this:

I have to express the following as a number in the form a/b, assuming a and b are integers.

-2^4 + 3^-1

I know that to get rid of the negative exponent I need to make it 1/3^1. However, I cannot seem to figure it out completely. Any help would be appreciated.

You have this

$\displaystyle -2^4+\frac{1}{3}$

Now compute 2 to the forth power and then get a common denominator and add.
• Jun 2nd 2011, 04:35 PM
Chevytuff19
Quote:

You have this

-2^4+\frac{1}{3}

Now compute 2 to the forth power and then get a common denominator and add.
I did it this way and came up with \frac{49}{3}

I know the correct answer is \frac{47}{3} , though.

I have tried to reverse engineer it for a while now, but can't seem to figure out exactly where I am messing it up. I am sure this is a very simple mistake I am making since I did the other questions in the same section without much trouble.

Also, any idea why my fraction tag isn't working? :)
• Jun 2nd 2011, 04:48 PM
Chevytuff19
Do I need to change the + sign to a - sign when I am making the exponent positive?
• Jun 2nd 2011, 05:06 PM
TheEmptySet
Quote:

Originally Posted by Chevytuff19
Do I need to change the + sign to a - sign when I am making the exponent positive?

You need to follow the order of operations. So you do exponents first

$\displaystyle -2^4+3^{-1} \iff -16+\frac{1}{3}$

Now you need to get a common denominator

$\displaystyle -16 \cdot \frac{3}{3}+\frac{1}{3}=...$

Can you finish from here?
• Jun 2nd 2011, 05:13 PM
Chevytuff19
That makes sense now that I look at it...I forgot that {-2}^{ 4} is different than {(-2)}^{4 } . I was using 16 instead of -16. Thanks for the help!