Question

I need help refreshing my memory on how to simplify these fractions with a rational exponent in denominator. Will give MEDAL!

Answer 1

\[\frac{ 1 }{ t ^{5/2} }\]

Answer 2

\[\frac{ 1 }{ 2t ^{5/2} }\]

Answer 3

do they want you to convert to radical form?

Answer 4

well, for the second fraction the answer is: \[\frac{ 1 }{ t ^{2}\sqrt{t} }\] I want to know how to get to that point.

Answer 5

oh I gotcha

Answer 6

rule:
\[\LARGE x^{m/n} = \sqrt[n]{x^m}\]

in this case, m = 5 and n = 2

\[\LARGE x^{5/2} = \sqrt[2]{x^5}\]
\[\LARGE x^{5/2} = \sqrt{x^5}\]

Answer 7

then you simplify the radical

\[\Large \sqrt{x^5} = \sqrt{x^4*x}\]
\[\Large \sqrt{x^5} = \sqrt{x^4}*\sqrt{x}\]
\[\Large \sqrt{x^5} = x^2\sqrt{x}\]

Answer 8

that makes sense to me now! thank you!

Answer 9

do you see what to do next?

Answer 10

well I guess it depends on the book, so it's optional, but some books rationalize the denominator

to do that, you'd multiply top and bottom by sqrt(t)


\[\Large \frac{ 1 }{ t ^{2}\sqrt{t} } = \frac{ 1*\sqrt{t} }{ t ^{2}\sqrt{t}*\sqrt{t} }\]

\[\Large \frac{ 1 }{ t ^{2}\sqrt{t} } = \frac{ \sqrt{t} }{ t ^{2}*t }\]

\[\Large \frac{ 1 }{ t ^{2}\sqrt{t} } = \frac{ \sqrt{t} }{ t ^{3} }\]