Question

what's the easiest way to remember how to do exponents like this (3m^-2n^4)^-2 because i can not remember and i keep messing up.

Answer 1

\[(3m ^{-2}n ^{4})^{-2}\]?

Answer 2

yes

Answer 3

Well, the main thing is if the exponent is negative, flip it upside down to make it positive. If you want it negative, flip it upside down. So in this example, absolutely everything is taken to a -2 power. Me personally, I'd probably distribute it first. See if this part makes sense first. I'm going to multiply the -2 into the exponents insidwe of the parenthesis:
\[(3m ^{-2}n ^{4})^{-2}=3^{-2}m ^{-2*-2}n ^{4*-2}\]It literally can multiply in. So this I'll simplify:
\[3^{-2}m ^{4}n ^{-8} \]
can ya kinda see what i did?

Answer 4

kinda

Answer 5

oh yeah okay

Answer 6

i see now

Answer 7

i have another one that i'm not so good at also kinda the sam but different

Answer 8

Well, basically when you have powers that are being raised to another power. The 3 had a first power, the m had a -2 power and the n had a -4 power. All of those were being raised to a -2 power on the outside. When that happens you can multiply all the powers. And alright, cool. Now when you have a negative exponent, you can flip it upside down to make it positve. For example:
\[x ^{-3}=\frac{ 1 }{ x ^{3} }\]
\[\frac{ 2 }{ x ^{-2} }=2x ^{2} \]
\[\frac{ x ^{-2} }{ y ^{-4} }=\frac{ y ^{4} }{ x ^{2} }\]
\[(2x)^{-3}=\frac{ 1 }{ (2x)^{3} } \]
These are just a bunch of examples. We can finish your problem of course, but if you see anything awkward or have a question about any of it, definitely say so.

Answer 9

okay i see

Answer 10

So that's exactly what we can do with what we have left from your problem:
\[\frac{ m ^{4} }{ 3^{2}n ^{8} }\]If it was negative, I moved it down, the m was positive, so I kept it on top.

Answer 11

okay i understand this one can you give me another problem and see if i can do it on my own

Answer 12

Well, there's one last thing we have an option of doing.

Answer 13

okay

Answer 14

Now imagine those weren't exponents, but were just numbers being multiplied like this:
\[(4m-8n)\]You could factor a number out of that, right?

Answer 15

yes. it would be 4m-8n or the factors would be 4 and 2

Answer 16

Well, you could make it like this: 4(m-2n). Have you seen stuff like that before?

Answer 17

no i have not i'm new to this stuff

Answer 18

Alright then, no problem :) Basically, there is a way to putit back in the same way we started. So instead of the factor business, let me reshow you the problem. You think you understand what we've done so far?

Answer 19

yes, okay

Answer 20

do you want me to see how to put it back in?

Answer 21

Alright. So this is back to what we started with:
\[(3m ^{-2}n ^{4})^{-2} \]Now I thought it best to start out with multiplying that -2 on the outside to show you, but it is not necessary. We can move things around just as is. I was just thinking this might have been more confusing at first. Alright, so that -2 that is on the outside of everything. I'll make that positive to start, so let's flip that to the bottom of a fraction:
\[\frac{ 1 }{ (3m ^{-2}n ^{4})^{2} } \]