Rewrite in simplest radical form X^5/6 over x^1/6
Show each step of your process.

- anonymous

Rewrite in simplest radical form X^5/6 over x^1/6
Show each step of your process.

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- anonymous

@lizz123

- lizz123

@Ashleyisakitty

- lizz123

@jim_thompson5910

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## More answers

- anonymous

@KEYS

- jim_thompson5910

|dw:1434411658371:dw|

- jim_thompson5910

|dw:1434411694412:dw|

- jim_thompson5910

since the bases are the same (both x), we can subtract the exponents (top - bottom)
|dw:1434411735859:dw|

- jim_thompson5910

|dw:1434411774461:dw|

- jim_thompson5910

I'll let you finish up

- anonymous

x^4/6

- anonymous

yes? @jim_thompson5910

- jim_thompson5910

you can then reduce 4/6 to get what?

- anonymous

2/3

- jim_thompson5910

correct
|dw:1434412037037:dw|

- anonymous

But we aren't done right?

- jim_thompson5910

that's the final answer

- jim_thompson5910

we can't reduce 2/3 any further

- anonymous

|dw:1434412118662:dw|

- jim_thompson5910

ah they want you to convert to radical form

- jim_thompson5910

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

- jim_thompson5910

m = 2
n = 3
\[\LARGE x^{m/n} = \sqrt[n]{x^m}\]
\[\LARGE x^{2/3} = \sqrt[3]{x^2}\]

- anonymous

Okay:) Thank-you. Mind if I ask another?

- jim_thompson5910

sure go ahead

- anonymous

Is the expression x3â€¢x3â€¢x3 equivalent to x3â€¢3â€¢3? Why or why not? Explain your reasoning.

- jim_thompson5910

what are your thoughts on it

- anonymous

|dw:1434412295575:dw|

- anonymous

That was the first equation, if u can read it

- anonymous

|dw:1434412377772:dw|

- anonymous

That's the 2nd one.

- jim_thompson5910

what are your thoughts on this? were you able to get started at all?

- anonymous

Ok so I don't think they are equal

- jim_thompson5910

and why is that?

- anonymous

because one is x^27

- anonymous

and I don't know about the other.

- jim_thompson5910

|dw:1434412588940:dw|

- jim_thompson5910

the first one, you use the rule
\[\Large x^a*x^b = x^{a+b}\]

- jim_thompson5910

and you can extend out the rule
the rule basically says "if the bases are the same, then you add the exponents"
|dw:1434412649041:dw|

- jim_thompson5910

|dw:1434412662937:dw|

- jim_thompson5910

Or you can replace x with some small number, say x = 2
then compute x^3*x^3*x^3 and x^(3*3*3) to see if they are equal or not

- anonymous

x^9 for the second equation right?

- jim_thompson5910

|dw:1434412780279:dw|

- anonymous

So they aren't equal? Right?

- jim_thompson5910

yeah first one is x^9 the second is x^27

- jim_thompson5910

I would also use numbers in place of x to test too

- anonymous

Ok! That's a good idea!! :)

- anonymous

I have two more questions, and I'm done. Please?

- jim_thompson5910

I'll help with one more

- anonymous

Thank you:)

- anonymous

Which of the following expressions are equivalent? Justify your reasoning.
A. 4âˆšx3
B. 1/ xâˆ’1
C. 10âˆšx^5â€¢x^4â€¢x^2
D. x^1/3 times x^1/3 times x^1/3

- anonymous

@jim_thompson5910

- jim_thompson5910

can you draw out answer C? it's hard to tell where the root ends

- anonymous

It's over the whole thing, except the 10

- jim_thompson5910

so it is \[\Large 10\sqrt{x^5*x^4*x^3}\] ???

- anonymous

Yes

- jim_thompson5910

what does \[\Large x^5*x^4*x^3\] simplify to?

- anonymous

x^11

- jim_thompson5910

close

- jim_thompson5910

oh wait I have the wrong digit

- jim_thompson5910

it should be \[\Large 10\sqrt{x^5*x^4*x^2}\]

- jim_thompson5910

so yeah, 11

- jim_thompson5910

ok I see the answer now

- jim_thompson5910

what does x^1/3 times x^1/3 times x^1/3 simplify to?

- anonymous

x^3/3

- jim_thompson5910

the 3/3 turns into 1/1 or just 1
x^1 = x

- jim_thompson5910

so in the end, x^1/3 times x^1/3 times x^1/3 turns into just x

- jim_thompson5910

does choice B say this
\[\Large \frac{1}{x^{-1}}\]
??

- anonymous

yes

- jim_thompson5910

so,
\[\Large \frac{1}{x^{-1}} = \frac{1}{1/x} = \frac{x}{1} = x\]

- anonymous

Ok

- anonymous

so, b and d basically

- jim_thompson5910

yes

- anonymous

Thank-you so much for all your help:)

- jim_thompson5910

yw

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