simplest radical form
1
----
−3
over
x6

- anonymous

simplest radical form
1
----
−3
over
x6

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- anonymous

|dw:1438357564010:dw|

- anonymous

|dw:1438357606356:dw|

- anonymous

|dw:1438357606756:dw|

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## More answers

- OregonDuck

you are right

- anonymous

|dw:1438357635372:dw|

- anonymous

i think you are right. Did u see the picture @OregonDuck

- OregonDuck

yes i asked my older brother he said so

- Nnesha

is it your question \[\huge\rm \frac{ 1}{ x^\frac{ -3 }{ 6 }}\]
or \[ \huge
\frac{ \frac{ -1 }{ 3 } }{ x^6 }\] which one is right ?

- anonymous

the last one.

- Nnesha

-1/3 divided by x^6 right ?

- anonymous

um.. its the first one actually

- Nnesha

alright we already solved this question i guess 5 days ago.. hmm :=)
well first of all reduce the fraction

- Nnesha

-3/6= ?

- anonymous

-1/2

- Nnesha

yes right now apply exponent rule \[\huge\rm x^{-m} = \frac{ 1 }{ x^m }\]

- anonymous

soo....... 1/ X-1/2

- anonymous

yes

- Nnesha

well there you can't leave the *negative exponent * so that's why apply that exponent rule move x^-1/2 at the top

- Nnesha

\[\huge\rm \frac{ 1 }{ x^{-m} } = x^m\] example

- anonymous

@nerlineg in other words flip the fraction

- Nnesha

well not the exponent one :3

- anonymous

when one of you are done here can you help me?

- anonymous

wait the probelm is 1 over M|dw:1438358345252:dw|

- Nnesha

so that's why i didn't use *flip the fraction*
first step reduce the fraction you get \[\huge\rm \frac{ 1 }{ x^\frac{ -1 }{ 2} }\]

- anonymous

ok i understand that

- Nnesha

|dw:1438358519321:dw|
flip 1/x^{-1/2) fraction not just -1/2

- anonymous

so is it already flipped in your pic^^^^^ or you haven't done it yet

- Nnesha

do you know why we have to do that ?

- Nnesha

we need *positive exponent*

- anonymous

yeah, it's a negative and you cant have a negative.

- Nnesha

yes right

- anonymous

@jcoury how was i being mean? lol

- anonymous

okhay then whats next?

- Nnesha

alright so now flip the fraction *exponent rule* \[\huge\rm \frac{\color{Red}{ 1} }{\color{red}{ x}^\frac{ -1 }{ 2} }\]

- anonymous

you want me to flip that?

- anonymous

@nerlineg check your messages

- Nnesha

yes i changed that color so u can understand :3

- anonymous

|dw:1438358973582:dw|

- Nnesha

yayay that's right

- Nnesha

now you can convert 1/2 exponent to square root

- anonymous

over one is the same thing as no fraction though

- Nnesha

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

- anonymous

|dw:1438359068326:dw|

- Nnesha

well no..

- anonymous

this is how my teacher tough me to write it.. is this right?

- Nnesha

x^1/2 = whata ?

- anonymous

@nerlineg the ^1 needs to be inside the radical

- anonymous

|dw:1438359204293:dw|

- anonymous

|dw:1438359185853:dw|

- Nnesha

\[\huge\rm \frac{ x^\frac{ 1 }{ 2 } }{ 1 } = x^\frac{ 1 }{ 2 }\]
doesn't matter if you write one or not at the denominator so forget about one
now you just have \[\huge\rm x^\frac{ 1 }{ 2 }\]

- Nnesha

convert \[\huge\rm x^\frac{ 1 }{ 2 }\] to square root of x

- anonymous

|dw:1438359295654:dw|

- Nnesha

right but simple radical signs means square root so you don't need to write 2

- anonymous

so did i learn it the wrong way?

- Nnesha

\[\huge\rm x^\frac{ 1 }{ 2 }= \sqrt{2}\]

- Nnesha

\[\sqrt{ } \] <-square root

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @Nnesha
\[\huge\rm x^\frac{ 1 }{ 2 }= \sqrt{2}\]
\(\color{blue}{\text{End of Quote}}\)
correction:
\[\huge\rm x^\frac{ 1 }{ 2 }= \sqrt{x}\]

- anonymous

ohok can i also have it both ways??

- Nnesha

both ways ?

- Nnesha

do you mean this one ?|dw:1438359494260:dw|

- anonymous

yess

- Nnesha

no that's *mathematically * wrong
simple radical signs means square root

- anonymous

@nerlineg that's the answer

- anonymous

yeah you don't need a two next to the radical

- anonymous

|dw:1438359650632:dw|

- Nnesha

you don't even need one
one is invisible so \[\sqrt{x}\] is perfect

- anonymous

okhay i have one last question
s the expression x3•x3•x3 equivalent to x3•3•3?

- anonymous

i thiink the answer is no .b.c you need a base

- Nnesha

is it \[\huge\rm x^3 \times x^3 \times x^3\] equal to \[x^3 \times 3 \times 3 \] ?

- Nnesha

yes right now bec when you multiply same bases you should add their exponents \[\huge\rm x^m \times x^n \times x^z = x^{m+n+z}\]

- anonymous

nooo

- anonymous

wait.

- Nnesha

i got you

- Nnesha

is it \[\huge\rm x^3 \times x^3 \times x^3\] equal to \[x^{3 \times 3 \times 3} \] ?

- anonymous

|dw:1438360101001:dw|

- Nnesha

ye so when you multiply same bases you should *add* their exponents

- anonymous

the three are exponents

- Nnesha

yes i got it :=)

- anonymous

so the answer is no their not equal ?

- Nnesha

yes right

- anonymous

great job for helping :) i which their wasn't a limit on these golden medals :/

- anonymous

if i need any more help i'll tag you!

- Nnesha

sure
&thanks!

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