Question

Simplify each expression. Use positive exponents.
(x–2y–4x3) –2

Answer 1

\[(x-2y-4x^3)^{-2}\]Yes?

Answer 2

yes

Answer 3

Whenever you have a negative exponent, you can write it as the reciprocal of the base. This is usually stated this way:\[a^{-n}=\frac{1}{a^n}\]
We can use this to write\[(x-2y-4x^3)^{-2}=\frac{1}{(x-2y-4x^3)^2}\]

Answer 4

Depending on how your teacher wants you to simplify, that may be a fine answer. However, we can expand this out also.
\[\frac{1}{(x-2y-4x^3)^2}=\frac{1}{(x-2y-4x^3)((x-2y-4x^3)}\]\[=\frac{1}{x(x-2y-4x^3)+(-2y)(x-2y-4x^3)+(-4x^3)(x-2y-4x^3)}\]
You can use the distributive property again from there to simplify it even further.

Answer 5

She just said to simplify using positive exponents.

Answer 6

@kmorgan

Answer 7

looks the op has just copy pasted from her assignment page haha!
more like :
\[\large \left(x^{-2}y^{-4}x^3\right)^{-2}\]

Answer 8

...oh
lol

Answer 9

That makes more sense. Thanks @ganeshie8

Answer 10

@dwatts158 Is the problem written the way ganeshie8 wrote it?

Answer 11

yes

Answer 12

Okidoki. When you have a term raised to a power, you can multiply the exponents together. This property is usually written this way:\[(a^m)^n=a^{mn}\]
We can use this to write \[(x^{-2}y^{-4}x^3)^{-2}=x^{(-2)(-2)} y^{(-4)(-2)} x^{(3)(-2)}\]

Answer 13

*Basically, you can multiply those exponents together

Answer 14

Okay with that so far?

Answer 15

not really..... I am just confused

Answer 16

I am confudes cause She ask that we use positive exponents.

Answer 17

This is a step along the way. The use of only positive exponents is only one part of what is being asked for. The bigger part is simplifying. That always makes it difficult to understand what people are supposed to do with these problems. It would be better written as "SIMPLIFY using only positive exponents."

Answer 18

Let's take a step back :)
Suppose you have \[a^4a^5\]How would you simpify that?

Answer 19

Let's expand it out. a to the fourth power is just "a" multiplied 4 times. We can rewrite it this way:
\[a^4a^5\]\[(aaaa)(aaaaa)\]\[a^9\]

Answer 20

ok

Answer 21

So, as a shortcut, when we multiply things with the same base together, we can just add the exponents:
\[x^{10}x^4=x^{14}\]\[y^9y^7=y^{16}\]\[b^5b^{-2}=b^3\]

Answer 22

Okay with that idea?

Answer 23

Yes you explain it so well.

Answer 24

Thanks :)
Let's go back to your problem for a moment.
\[(x^{-2}y^{-4}x^3)^{-2}\]Ignore the fact that there are negative exponents, and ignore the fact that there is a "y" in there. See those two "x" parts? Try combining those together. Simplify \[x^{-2}x^3\]

Answer 25

x-5

Answer 26

Ah, when you add -2 and 3, you get 1. That will give you x^1

Answer 27

ok

Answer 28

Okay. Now we have\[(x^1y^{-4})^{-2}\]
Let me say a couple things about this.

First, these problems are going to be easier if you write the exponents that usually aren't written in there. For example, rewrite x as "x^1" like I did.

Second, you can't combine an x and a y. For example, what I'm about to do is WRONG:
\[x^1y^{-4}=xy^{-3}\]It just simply doesn't work like that. You can ONLY combine them if they have the same BASE.

Answer 29

Now, let's talk about raising a term to a power. Let's say we have (a^3)^4:
\[(a^3)^4=a^3a^3a^3a^3\]Now each of these has the same base, so we can ADD the exponents.
\[(a^3)^4=a^{3+3+3+3}=a^{12}\]
New Rule: If we raise a power to a power, we MULTIPLY the exponents.
Examples:\[(a^5)^4=a^{20}\]\[(g^9)^{10}=g^{90}\]\[(z^{-2})^{-2}=z^4\]
Also, notice the difference between these two:
\[a^4a^5=a^9\]\[(a^4)^5=a^{20}\]

Answer 30

And, unfortunately, I do need to go now. Let me finish out the rest of the problem.
\[(x^1y^{-4})^{-2}=x^{-2}y^8\]
No negative exponents, so we use the property from my first response at the very beginning.
\[x^{-2}=\frac{1}{x^2}\]
This gives us \[x^{-2}y^8=\frac{y^8}{x^2}\]
So your answer is \[\frac{y^8}{x^2}\]Sorry I can't stay longer to help, but other people can help if you need to repost this problem :)

Answer 31

thank you