how do you rationalize this denominator?

- AngelaB97

how do you rationalize this denominator?

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- chestercat

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

- 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.