# Exponents Expressed As Roots

• Jun 21st 2012, 06:45 AM
allyourbass2212
Exponents Expressed As Roots
With an exponent you can express it as a .....

Original Exponent: $7(5)^\frac{1}{2}$
$=17.5$

Express it as a fraction: $\frac{7}{5^\frac{-1}{2}}}$
$=17.5$

Express it as a root: $7\sqrt{5}$
plugging the above into a calculator yields $15.65$. Did I do something incorrect, shouldn't it equal $17.5$ like the other examples? Am I doing something incorrectly? Thanks
• Jun 21st 2012, 06:57 AM
Reckoner
Re: Exponents Expressed As Roots
Quote:

Originally Posted by allyourbass2212
Express it as a root: $7\sqrt{5}$
plugging the above into a calculator yields $15.65$. Did I do something incorrect, shouldn't it equal $17.5$ like the other examples? Am I doing something incorrectly? Thanks

Yes, I think you are not using your parentheses correctly in the first two expressions.

$7\cdot5^{1/2} = \frac7{5^{-1/2}} = 7\sqrt5\approx15.652.$

What you were probably calculating was

$7\cdot\frac{5^1}2 = 17.5,$

which is how your calculator would interpret 7*5^1/2 if you don't put parentheses around the exponent (remember that exponents have higher precedence than division in the order of operations).