SOLUTION: This problem is throwing me off because of the negative exponent. If you are able to answer please show your work so I will understand how you arrived at the answer for my other ho

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: This problem is throwing me off because of the negative exponent. If you are able to answer please show your work so I will understand how you arrived at the answer for my other ho      Log On


   

Question 374383: This problem is throwing me off because of the negative exponent. If you are able to answer please show your work so I will understand how you arrived at the answer for my other homework problems. Thanks so much!!!
3^5/8
______
3^-1/8
(note: this is a fraction with 3^5/8 being the numerator and 3^-1/8 being the denominator)

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%285%2F8%29%2F3%5E%28-1%2F8%29
The rules for exponents are the same all exponents. The fact that there are fractional and/or negative exponents do not change the rules! This is a division involving the same base, 3. The rule here is to subtract the exponents (the numerator's exponent minus the denominator's exponent). Applying this rule to your expression we get:
3%5E%28%285%2F8%29-%28-1%2F8%29%29
or
3%5E%28%285%2F8%29%2B%281%2F8%29%29
Fortunately the two fractions have the same denominator so we can go ahead and add them:
3%5E%286%2F8%29
The fraction will reduce:
3%5E%283%2F4%29
This may be an acceptable answer. But we can rewrite this using the fact that a%5E%28p%2Fq%29+=+root%28q%2C+a%5Ep%29:
root%284%2C+3%5E3%29
Since 3%5E3+=+27 this becomes:
root%284%2C+27%29