Question

. Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
-18xy^5/54x^3y^6

Answer 1

you can simplify the numerical part (the "-18" and "54") like a normal fraction (-18/54)... look for common factors in numerator and denominator and cancel them.

Answer 2

3 is common in both

Answer 3

-1/3

Answer 4

right... actually... if you notice, 18 is common in both.... 3 x 18 = 54

So you could cancel out 18 from the top, leaving 1, and from the bottom, leaving 3

(oh, you beat me to it...)

Answer 5

So, it's the same thing for the variables. You have x on top and x^3 on bottom

Answer 6

cancel to leave x^2 on bottom.

Answer 7

y^5 on top, and y^6 on bottom... cancel to leave just y on the bottom

Answer 8

overall, looks like -1/(x^2y)

Answer 9

would it be 1y or 11y

Answer 10

I don't understand...\[\frac{ y ^{5} }{ y ^{6} } = \frac{ 1 }{ y }\]

Answer 11

-1/3x^2y

Answer 12

this is the answer

Answer 13

\[-\frac{ 1 }{ 3x ^{2}y }\]

Answer 14

ok thank u

Answer 15

yes, I got confused when you asked something about 11y

Answer 16

yea i get confused on if you add or subtract the variables

Answer 17

oh, ok....

if it's a fraction with variables with exponents, then think of it like this for like y^5/y^6:
\[\frac{ (y)(y)(y)(y)(y) }{ (y)(y)(y)(y)(y)(y) }\]

Answer 18

so you just think to yourself... "I have 5 y's on top, and 6 on the bottom, so I will cross out 5 from each, leaving just one y on the bottom."

You could also describe that as "subtracting the exponents", as in, you will subtract the exponent 5 on the top y's from the exponent 6 on the bottom y's, leaving just y^1 on the bottom, since 6-5 is 1.

This is why the question told you to answer with POSITIVE exponents...

You COULD (if you wanted) cancel the other way, subtracting the 6 exponent on the bottom from the 5 on the top, leaving -1 on the top.... and y^(-1) just happens to be = 1/y^1 so you get the same thing, but expressing the answer as POSITIVE exponents is "cleaner"

Answer 19

so as positive it is no - answers

Answer 20

if you had ended with x^(-2)y^-1, it would have been correct but wrong form

Answer 21

correct value, but using negative exponents

Answer 22

so the answers is - also this is were i really get lost.

Answer 23

Oh!!! no... different!!

Answer 24

It's fine that the whole thing is negative... they just didn't want you to answer like the following:

Answer 25

\[-\frac{ x ^{-2}y ^{-1} }{ 3 }\]

Answer 26

can you help me with another one

Answer 27

Short Answer: Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
(5x-1)-3

Answer 28

That is equivalent to what we had above, but using negative exponents... if you had done it that way, you "move" the x^(-2) to the bottom by multiplying top and bottom by x^2, cancelling the x^(-2) on top and leaving x^2 on bottom...

Answer 29

did you leave out the exponent part of that 2nd problem?

Answer 30

or is that written correctly?

Answer 31

(5x^-1)^-3

Answer 32

125/x^3 is this right

Answer 33

So, that is really like:
\[(5\frac{ 1 }{ x })^{-3} = \frac{ 1 }{ (\frac{ 5 }{ x })^{3} }\]

Answer 34

ok

Answer 35

let me double check that...

Answer 36

easier: 5x^-1 is just 5/x

so (5x^-1)^(-3) is (5/x)^-3 which is equal to (x/5)^3

Answer 37

So it would be x^3 / 125

I think that's it, anyway...

bad to hurry, need to make sure you don't flip the fraction over too many times while playing with that negative exponent

Answer 38

ok i switch it around

Answer 39

"raising to the negative 3rd power" means the same as "cubing and inverting"
\[x ^{-3} = \frac{ 1 }{ x }\]

Answer 40

ugg,,, that was supposed to be\[\frac{ 1 }{ x ^{3} }\]

Answer 41

ok

Answer 42

I just said that as a way of saying that neg exponents are sometimes confusing, but if you start to get confused, just rewrite as a fraction and "move" the neg exponent variable across the fraction (either from top to bottom or bottom to top) to make it a positive exponent

Answer 43

ok thanks for everything

Answer 44

no problem :) These are annoying to type with all the exponents... :)