Exponents Expressed As Roots

With an exponent you can express it as a .....

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

$\displaystyle =17.5$

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

$\displaystyle =17.5$

Express it as a root: $\displaystyle 7\sqrt{5}$

plugging the above into a calculator yields $\displaystyle 15.65$. Did I do something incorrect, shouldn't it equal $\displaystyle 17.5$ like the other examples? Am I doing something incorrectly? Thanks

Re: Exponents Expressed As Roots

Quote:

Originally Posted by

**allyourbass2212** Express it as a root: $\displaystyle 7\sqrt{5}$

plugging the above into a calculator yields $\displaystyle 15.65$. Did I do something incorrect, shouldn't it equal $\displaystyle 17.5$ 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.

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

What you were probably calculating was

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

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).