- AngelaB97

how do you rationalize this denominator?

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- AngelaB97

|dw:1441582663963:dw|

- caominhim

apply the sqaure root to top and bottom

- caominhim

oh is the the 7th root?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- caominhim

\[\sqrt[7]{\frac{ 1 }{ a^{2} }} = \frac{ \sqrt[7]{1} }{ \sqrt[7]{a^{2}} }\]

- jdoe0001

hmmm how would you rationalize ... say \(\bf \cfrac{1}{a^2}?\)

- nincompoop

it is up to you
\(\huge \frac{1^{\frac{1}{7}}}{(a^2)^\frac{1}{7}} \)

- AngelaB97

@nincompoop how would you work out the problem further?

- jdoe0001

by rationalizing, I assume you mean the exponent, as in \(\large a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad
\sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\)

- nincompoop

you can probably make it so there is no root in the denominator

- AngelaB97

the answer is supposed to be |dw:1441583091798:dw|

- AngelaB97

i just don't get how

- nincompoop

mathematicians decided that it is inelegant to have a root in the denominator so we are suppose to stroke their egos

- nincompoop

so multiply it by 1 that mimics the denominator

- nincompoop

you know how \(\huge \frac{c}{c} =1\) or any fraction that has the same numerator and denominator equals 1 with the exception of \(\large \frac{0}{0} \)

- nincompoop

were you told that's the answer by the book?

- nincompoop

|dw:1441583625914:dw|

- nincompoop

|dw:1441583819764:dw|

- nincompoop

|dw:1441583873041:dw|

- nincompoop

HELLOOOOOOOOO WHERE ARE YOUUUUUUUUUUUUUUUUU HELLOOOOOOOO ECHOOOOOOO

- nincompoop

HELLOOOOOOOOO ECHOOOOOOOOO
I think you fell into the mathematical abyss or black hole

- AngelaB97

okay i get what you did

- AngelaB97

however can you explain why the book only put the rad over the denominator and not the numerator...this is regarding the picute i attached up there

- nincompoop

i do not see it

- AngelaB97

|dw:1441588006576:dw|

- AngelaB97

why did they not put the rad sign over the 1 as well?

- nincompoop

\(\huge 1^\frac{1}{7} = 1\)

- nincompoop

the 7th root of 1 is 1 that is why

- AngelaB97

how I'm so sorry

- nincompoop

what is the square root of 1 ?

- AngelaB97

1

- nincompoop

what is the cube root of 1?

- nincompoop

also 1

- nincompoop

the trend follows

- AngelaB97

so anything to the nth root of 1 is 1

- nincompoop

nth root providing it is a positive whole number, pretty much

- nincompoop

I may need an actual mathematician to confirm this with proof, but that is what I know even tho I am not a mathematician

- AngelaB97

okay well thanks so much for your help! :)

- nincompoop

no problem
enjoy learning

- AngelaB97

thanks!

Looking for something else?

Not the answer you are looking for? Search for more explanations.