(x^-3)^-5x^6
a.x^21
b.x^-21
c.x^48
d.x^-48

- anonymous

(x^-3)^-5x^6
a.x^21
b.x^-21
c.x^48
d.x^-48

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- anonymous

@KeithAfasCalcLover can you help me again ?

- anonymous

I might ;)...What is the question?

- anonymous

:) . Thats all they gave me

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## More answers

- anonymous

@KeithAfasCalcLover

- anonymous

(x^-3)^-5x^6
a.x^21
b.x^-21
c.x^48
d.x^-48

- anonymous

Ehhh...lets see...Se the thing is that I don't know the syntax of the question...
I mean it could be:
\[(x^{-3})^{{(-5x)}^6}\]
or
\[(x^{-3})^{-5}*x^6\]

- anonymous

@KeithAfasCalcLover its the second one

- anonymous

Ahh that makes so much sense. Cool. So you know that:
\((x^a)^b=x^{ab}\) and
\(\frac{x^a}{x^b}=x^{a-b}\) and
\((x^a)(x^b)=x^{a+b}\)

- anonymous

So you can use these rules to simplify some terms. For instance:
\((x^{-3})^{-5}=x^{-3*-5}=x^{15}\)

- anonymous

And you should in the end get one term with the form:
\(x^p\) and Ill let you figure out \(p\) ;-)

- anonymous

@KeithAfasCalcLover Sooooo Maaaaany Leeettttersss :(

- anonymous

I know...isn't it beautiful ;-)
The three lines full of letters are called the "laws of exponents"

- anonymous

Not To Me It Isnt :/ i feel like i have dyslexia when i do algebra !

- anonymous

So like if I had something like \(x^2*x\), I could find out that that actually was \(x^2*x^1=x^{2+1}=x^3\).The laws are methods of simplifying exponents. And the higher you go in math, Like calculus and trigonometry and stuff, the more letters are used! Haha. Don't let the numbers trip you up though, they just mean a letter to hold the place of a number Which means that if you put ANY NUMBER in the equation, you can get an answer. For instance, using the example I used above, \(x^2*x=x^3\), Think of ANY NUMBER for x, and it'll be true. Sometimes it helps to put numbers into these rules and see that no matter what number you put, Its always true.

- anonymous

So lets say for:
\((x^a)(x^b)=x^{a+b}\) Think of ANY NUMBER for x,a, and b and youll see that it holds true!. So lets say
x=5,a=2, and b=8.
______________________________________
\((5^2)(5^8)=5^{10}\)
\((25)(390625)=5^{10}\)
\(9765625=5^{10}\)
______________________________________
And ill be willing to bet that \(5^{10}=9,765,625\)!

- anonymous

i understand that half but the question they gave me i just dont get @KeithAfasCalcLover

- anonymous

i think the answer is c. \[x^{48}\]

- anonymous

Im not saying its right or wrong but would you be able to show me how you got there? :-)

- anonymous

uhm i uhh lol .added the two exponents that were next to eachother the two negatives and it gave me 8 and i multiplied the 8 by the last exponent which was 6? \[(x ^{-3})^{-5}x ^{6}\] @KeithAfasCalcLover Help Me More ! im a slow learner

- anonymous

Alright well that one wasn't completely bang on but ill help you :-)
You have three..."things" being done to x:
You have \(x^{-3}\), You have all that \((x^{-3})^{-5}\) and then you have all that multiplied by \(x^6\), right?

- anonymous

yes @KeithAfasCalcLover

- anonymous

Would it be ok with you if I put:
\(a=-3\)
\(b=-5\)
\(c=6\)
??

- anonymous

Ya !

- anonymous

@KeithAfasCalcLover

- anonymous

So then we can rewrite this as:
\[(x^a)^b*x^c\]
Which is a little bit neater ;)
So then we know that \((x^a)^b=x^{ab}\) so we can rewrite the equation:
\[(x^a)^b*x^c=x^{ab}*x^c\]. Cool? :-)

- anonymous

Yeah ! @KeithAfasCalcLover |dw:1377712167716:dw|

- anonymous

Great!
And we know that \(x^a*x^b=x^{a+b}\) So we can rewrite the whole thing as:
\[(x^a)^b*x^c=x^{ab}*x^c=x^{ab+c}\] And since we know what a,b,and c are, we can plug 'em in! Nice so far?

- anonymous

Yes @KeithAfasCalcLover

- anonymous

So we know a and b and c, so lets find out what exactly is : \(ab+c\)
\(ab+c=(-3)(-5)+6=15+6=21\)
So the answer is \(x^{21}\)!
Did all that make sense? :-)

- anonymous

yes ! you shouldve done that earlier lmbo ! @KeithAfasCalcLover

- anonymous

Haha but the thing is using the letters made things so much easier. And those basic laws will take you a long way! Well im glad you got it Deivyneee :-)

- anonymous

Lol :) Thank You @KeithAfasCalcLover

- anonymous

My Pleasure, @Deivyneee

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