Question

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

Answer 1

@KeithAfasCalcLover can you help me again ?

Answer 2

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

Answer 3

:) . Thats all they gave me

Answer 4

@KeithAfasCalcLover

Answer 5

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

Answer 6

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
\[(x^{-3})^{-5}*x^6\]

Answer 7

@KeithAfasCalcLover its the second one

Answer 8

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
\((x^a)(x^b)=x^{a+b}\)

Answer 9

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

Answer 10

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

Answer 11

@KeithAfasCalcLover Sooooo Maaaaany Leeettttersss :(

Answer 12

I know...isn't it beautiful ;-)

The three lines full of letters are called the "laws of exponents"

Answer 13

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

Answer 14

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.

Answer 15

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 \(5^{10}=9,765,625\)!

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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?

Answer 21

yes @KeithAfasCalcLover

Answer 22

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

??

Answer 23

Ya !

Answer 24

@KeithAfasCalcLover

Answer 25

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? :-)

Answer 26

Yeah ! @KeithAfasCalcLover

Answer 27

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?

Answer 28

Yes @KeithAfasCalcLover

Answer 29

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? :-)

Answer 30

yes ! you shouldve done that earlier lmbo ! @KeithAfasCalcLover

Answer 31

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 :-)

Answer 32

Lol :) Thank You @KeithAfasCalcLover

Answer 33

My Pleasure, @Deivyneee