Question

(x-2)^2/3=9

Answer 1

what is the exponent here? 2 or 2/3?

Answer 2

2/3

Answer 3

\[\large (x-2)^{\frac23}=9\]

Answer 4

yes.

Answer 5

That denominator in the exponent means cube root...

Answer 6

okay

Answer 7

So, in fact
\[\Large a^{\frac{m}n}=\sqrt[n]{a^m}\]

Answer 8

that looks like greek to me??

Answer 9

Really? Because this \(\alpha\theta\eta\nu\alpha\iota\omicron\sigma\) looks Greek to me ^.^

LOL

What I mean is that the denominator of the exponent means 'root'
So
\[\Large (x-2)^{\frac23}= \sqrt[3]{(x-2)^2}\]

Answer 10

is that how i solve beacuse i know how to answer that.

Answer 11

Really? Then yes, if it makes it easier for you, then do it like this :)
\[\Large \sqrt[3]{(x-2)^2}= 9\]

Answer 12

and solve ^.^

Answer 13

yeah but how do i switch it to that way?

Answer 14

You know how in a radical, this part
\[\huge \sqrt[\color{red}n]{a}\] is called the index?

Answer 15

yes and i got 733 im not sure that is correct.

Answer 16

When faced with exponents which, inconveniently, are fractions...
\[\huge a^{\frac{m}n}\] the denominator simply becomes the index, and the numerator, the exponent...
\[\huge = \sqrt[n]{a^m}\]

Answer 17

lol how'd you get 733?

Answer 18

honestly mathway.com....

Answer 19

i just have 2 days to pass a year of school.

Answer 20

Awww.... lol
tell you what, let's forget that, and get back to this
\[\huge (x-2)^{\frac23}=9\]
Why don't we raise both sides of the equation to an exponent 3?
\[\huge \left((x-2)^{\frac23}\right)^3=9^3\]

Answer 21

From the laws of exponents, you should get this...
\[\huge (x-2)^{\frac23 \cdot 3}=9^3\]

Answer 22

And what is 2/3 times 3?

Answer 23

6/9? not trying to be funny.

Answer 24

lol, there's a problem here...
when you multiply a fraction by a whole number, only do it to the numerator, and not both :)

Answer 25

so okay so 6/3 which is 2

Answer 26

Yup... so we get
\[\Large (x-2)^2 = 9^3\]

Answer 27

which is (x-4)=729 correct.

Answer 28

Why x - 4?

Answer 29

oh.. 4*4 which is 16

Answer 30

No, I'd actually suggest, you leave that as is
\[\Large (x-2)^2 = 729 \]
Now you may simply get the square root of both sides :D

Answer 31

If I'm not mistaken, the square root of 729 is 27...

Answer 32

So you'd get\[\Large x-2 = 27\]

Answer 33

so x= 25?

Answer 34

no, lol...
25 - 2 is 23, not 27 :P

Answer 35

but 27-2 is 25 how did you get 23?

Answer 36

Let's run that through again...
x - 2 = 27

if x is 25, then...
25 - 2 = 27
23 = 27
which simply isn't true lol



x - 2 = 27

We can simply add 2 to both sides...
x - 2 + 2 = 27 + 2

take it away, Chris ^.^

Answer 37

you put me on the spot... uhhhh 29? please be right.

Answer 38

Yup :)

Answer 39

oh my... tha was difficult. thank you @peterpan

Answer 40

And if you check with your fancy calculator, you'll find that 29 fits your original equation perfectly ^.^

\[\large (x-2)^{\frac23}=9\]

Answer 41

There is actually another answer, though...

Answer 42

your right.

Answer 43

oh... I am?
lol
of course I am XD

Answer 44

its multiple choice
–25
–25, 29
–27, 27
29

Answer 45

And you already answered?

Answer 46

And you sure are. :)

Answer 47

29

Answer 48

Wait, you confirmed?

Answer 49

and no.. i havent answered it yet.

Answer 50

well, hold it

Answer 51

Because there's another answer :P
\[\Large (x-2)^2 = 729\]

Answer 52

holding.

Answer 53

solving for 729?

Answer 54

While it is true that if \[\Large (x-2)^2 = 729\]
Then
\[\Large x-2 = 27\]
However, it may also be that
\[\Large x-2 = -27\]

I apologise on behalf of algebra for being so hazy when it comes to square roots, in general, you usually only take the positive square root, but when you're solving, you take both cases...
\[\Large (x-2)^2 = 729\]
\[\Large x-2 = \pm 27\]

We've already considered the case where 27 is positive, what about if it's negative?
\[\huge x -2 = -27\]

Answer 55

Much like earlier, we simply add 2 to both sides...
so...

x - 2 + 2 = -27 + 2
... encore, Chris?
What's x, this time around?

Answer 56

-25

Answer 57

so its -25,29?

Answer 58

And you'll find that that value for x also fits the original equation :)

Answer 59

Yup, that's the one

Answer 60

so much work. for 2 numbers. who taught you because they deserve a pat on the back.

Answer 61

My maths teacher... she's pretty brilliant...and pretty pretty :D

Answer 62

thats a bonus. hahaha well thank you sir. hope to see you again on here.

Answer 63

Anytime... (I'm here)

Answer 64

okay i got one more. im pretty sure im right

Answer 65

will you check it for me?

Answer 66

sure :)

Answer 67

which expression is the exponetial form of \[\sqrt[3]{m}\]

Answer 68

oh... I think we got this covered :D
What's your answer?

Answer 69

m^3

Answer 70

Nope :)
I told you, the index of the radical goes at the DENOMINATOR of the exponent ^.^

Answer 71

theres just a 3...

Answer 72

or is the denominator m

Answer 73

its m^1/3

Answer 74

3 is the index of the radical, so yeah, \[\huge m ^{\frac13}\]
That's it :D

Answer 75

woooooooooooooooooo!!!! im getting smarter. your awesome

Answer 76

You're awesome :)

Answer 77

:)